Optimal Design of Mixed-Media Packet-Switching ... - IEEE Xplore

158

IEEE TRANSACTIONS COMMUNICATIONS, ON

VOL. COM-25, NO. 1 , JANUARY 1977

Optimal Design of Mixed-Media Packet-Switching Networks: Routing and Capacity Assignment AND

FRANKLIN F KUO, FELLOW, IEEE

Absrruct-This paper considers a mixed-media packet-switched computer communication network which consists of a lowdelay terrestrial store-and-forward subnetcombined withalow-costhigh-bandwidth satellite subnet. We show how to route traffic via ground and/or satellite links by meansof static, deterministicprocedures and assign capacities to channels subject to a given linear cost such that the network average delay is minimized, Two operational schemes for this network model are investigated: one is a scheme in which the satellite channel is used as a slotted ALOHA channel; the other is a new multiaccess scheme we propose in which whenever achannel collision occurs, retransmission of the involved packets will route through ground links to theirdestinations. The performance of both schemes is evaluated and compared in terms of cost and average packet delay tradeoffs for some examples. The results offer guidelines for the design and optimal utilization of mixed-media networks.

packet-switched data service in which initially terrestrial and eventuallysatellitelinks will be available. Therefore, it is of great interestandimportanceto investigate, orat least to extend the current knowledge to cover, such amixed-media packet-switched computer communication network. Ourmixed-medianetworkmodel consistsofaterrestrial store-and-forward packet-switching network, referred to here as the ground subnet, andamultiaccess/broadcastsatellite which, together with the associated SIMP’s, forms the satellite subnet. The store-and-forward ground subnet can be implemented to provide a low delay by using, for example, leased lines of low errorrate.This, however, makesthenetwork necessarily expensive. The satellite subnet, on the other hand, is subject totheintrinsicpropagation delay ofabout 0.26 I. INTRODUCTION seconds, but its cost per channel bandwidth is substantially less than that of the groundlinks. Therefore,thecombinaN recent years two major packet-switched communication tion ofhigh-delaylow-costsatellite subnetthatoperates in techniques are becoming increasingly important in the decontentionmode andalow-delayhigh-costground subnet sign of large computercommunicationnetworks:onetechthat operates in queueing mode into an overall system model nique is to store-and-forward packetsover terrestrial communipresents many interesting problems. cation links; the other technique is t o transmit packets over a It is our goal in this paper t o examine a number of key random multiaccess radio or satellite channel. issues in the design of theproposed mixed-media packetUp to the present, the studies and implementations have switching network. Assuming thatnetworktopologyand networks utilizing solely eitherterrestrial beencenteredon traffic characteristics are given, we concentrate ?n the fol[e.g., Advanced Research Projects Agency Network lowing problems in the present paper: 1) routing of packets (ARPANET), National Physical LaboratoryDataNetwork via ground or satellite links; 2) capacity assignments for [ l ] , etc.] or satellite (e.g., ALOHANET) links. Recently ground and satellite channels; and 3) retransmission strategies. ARPA has augmented its terrestrial network with packetsatelRoutingprocedures have beeninvestigated using various lite communication between the US.and the UnitedKingdom approaches [4] -[7] . The routing we will consider is a detervia INTELSAT IV using satellite interface message processors ministic procedure, which optimizes the overall average packet (SIMP’s) built by Bolt Beranek and Newman Inc. (BBN) [ 2 ] . delay given a set of link capacities and message traffic characThis multiple-access broadcast system was initiated in Septemteristics. This is the approach taken byKleinrock [4], Felperin to includefourgroundstations ber 1975 andisexpected [ 5 ] , Fultz [ 6 ] ,and Cantor and Gerla [7] in their studies on shortly. TELENET Communication Corporation, one of the optimal determi:nistic routing for a terrestrial store-andnew value-added carriers [3], announced a plan t o offer public forward network; their results will be used here to obtain the optimalroutingforour mixed-media networkmodel. A Manuscript received March 24, 1976; revised September 15, 1976. capacity assignment problem in communication networks This work was supported in part by the ALOHA System,a research project at theUniversity of Hawaii, which is supported by the Advanced was first formulated by Kleinrock [4] , who assumed the linear Research Projects Agency, Department of Defense, and monitored by cost model and a continuum of channel capacities. We solve NASA Research Center under Contract NAS2-8590. our capacity assignment problem using the same approach and D. Huynh was withthe ALOHA System, University of Hawaii, find tradeoffs between cost and overall average packet delay. Honolulu, HI 96822. Heis now with IBM SystemCommunications Division, Kingston, NY 12401. We also investigate twooperational schemes for satellite H. Kobayashi was with the University of Hawaii, Honolulu,HI channels: one is aschemein whichthe satellitechannel is 96822, as a Consultant to the ALOHA System Project, on leave from used as a slotted ALOHA channel as discussed by Kleinrock the IBM Tbomas J. Watson Research Center, Yorktown Heights, NY 10598. and Lam [8], [9] ; the other is a new multiaccess scheme we F. F. Kuo was with the University of Hawaii, Honolulu, HI 96822. propose, in whic:h no retransmissions are attempted via satelHe is now with the Office of the Secretary of Defense, Washington, DC lite channel; whenever a channel collision occurs, retransmis20301.

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HUYNH e t a l . : DESIGN O F MIXED-MEDIA PACKET-SWITCHING NETWORKS

Sion of the involved packets will route through ground links t o their destinations. These two different schemes will be compared in terms of such performancemeasures as overall average delay of a packet, maximum allowable traffic loads, capacity requirements, etc. The proposed network modelconsists of the following. 1) A setof store-and-forward IMP-like devices interconnected by capacity-limited ground channels (a connected, distributedsubnet).Forthe sake of reliability thissubnet is at least two-connected. 2 ) A set of SIMP-like devices directly connected to satelliteground stations. These SIMP’s are usually geographically scattered and relatively far apart from each other. IMP’s and SIMP’s all have buffering and scheduling capabilities. 3) A multiaccess/broadcastsatellite transponder linking all SIMP’s in a star configuration. The SIMP’s together with the broadcast satellite channel will be referred to as a satellite subnet. Inthisnetworkmodel we assume thatthenetwork is regionalized. That is, the network is partitioned into regions, Each region contains a SIMP and a number of IMP’s. An IMP can only access its regional SIMP. In this study we assume that the number of SIMP’s and their locations are given a priori. A SIMP is usually colocated with an IMP at some node. The regionalization of IMP’s is determined by the closeness of an IMP t o a SIMP in terms of the number of hops and the distances between them. Such a structureis shown in Fig. 1. In the following, we first review previously known results which are important to our studies, and at the same time we developthose analyses which arc pertinentto our network model but have not been considered before. We then proceed on to formulateand solve the related design problems.

MULTI-~CESS/BROADCAST SATELLITE

.

Fig. 1.

Proposed network model.

* . *

ComputedPointsUsmg

Equation (2.2)

Thenumber associated witheach curve representsthenumber of SIMPS In

.

c

.

.* . .. . .

.. %

$

30

b

11. SATELLITE SUBNET MODEL

The satellite subnet consists of a set of SIMP’s which are linked together via a satellitemultiaccess/broadcast chanhel. Each SIMP is equipped with buffering and scheduling capabilties. The satellite channel model we will use is based upon the ALOHA technique of random-access synchronous timedivision multiplexing [ 101 , [ 1 11 . We assume throughout this study that the satellite channel is time-slotted [8], but as to multiaccessing methods, we consider twodifferent schemes: one is theslotted ALOHA, and theother is a new scheme which we namemultiaccesssatellite with terrestrial retransmission (MASTER).

Scheme I: Slotted ALOHA In our satellite subnet the user population consists of a set of SIMP’s, and we assume that each SIMP is provided with sufficiently large buffer capacity that new arrivals will never be blocked. Similarly a SIMP is capable of transmitting a new packet, even when previously sent packets are outstanding due t o collisions. study of slotted ALOHA Lam [9] hasmadeanextensive proposed for a satellite communication system. His result on a finite population model without blocking is given in terms of

20

lo

1

0‘

0

I

I

I

I

I

.2

.3

.4

I

1

.5

6

throughpi /pockefs/s/ofsJ

Fig. 2.

Comparisons of curves obtained by simulations in Lam [9] and by curve-fitting (2).

throughput-delay curves as shown in Fig. 2. These curves were obtained using simulation rather than by analysis and assumed equalinputratesfrom all users anduniformretransmission andreschedulingdelays. A reschedulingdelay results from a schedulingconflictinwhich one or more packets are scheduled t o transmit in a slot. The scheduling conflict is resolved by first sending the high-priority packet and rescheduling the other packets forlater slots. An important result from his simulation study is that when the satellite system has M = 10 users, itsthroughput-delaytradeoffsapproximatethose of an infinitely many user popuiation. If there were only one SIMP transmitting, i.e.,M = 1, then there should be no contention in the channel. Thus the delay

160

JANUARY COMMUNICATIONS, ON

TRANSACTIONS IEEE

1977

TABLE I

over the satellite subnet consists of the propagation delay and the average queueing delay; the latter component can be derived from the result of anM/D/1 queueing system:

PARAMETERS OF (2) #

where 7s

T

,

C,

x, (bits/packet). length 1/11,

~

average packet delay (seconds) 0.26 ~ second: delaytime due to propagation delay satellite channel capacity (bits/s) packet atransmission totalinputrateto (hence throughput rate from) the satellite channel (packets/s) packet

For M > 1 we found that a simple modification of (1) is very satisfactory to those curves obtained by simulation in a manner as indicated by Fig. 2. (2)

where a(M) represents the degradation factor of channel capacitydueto collision. From (1) and theknown result onan infinitepopulationmodel we have a(1) = 1 and lim M+w a(M) = l/e. The other parameter b(M) gives another degree of freedom for us t o fit the curves in the vertical direction. The set of parameters found are tabulated in Table I.

Scheme 11: MASTER

A possible drawback of the ALOHA scheme as applied to the satellite subnet is that each time a packet needs a retransmission, its delay time must be increased at least by the 0.26 seconds due to the inherent propagation delay of the satellite channel. Furthermore if the message traffic rate exceeds some critical level, the number of backlog packets will rise sharply, and will further increase theoccurrence of collisions. This positive feedback effect will possibly result in an avalanche of collisions: the channel utilization will rise up to almost 100 percent,yetthethroughput will suddenly drop to virtually zero. This “instability”problem of theslotted ALOHA is discussed by Kleinrock and Lam 191. Thisobservation had led us t o propose anew scheme, in which all retransmissions by SIMP’s are carried out through the ground subnet, and retransmittedpackets are reroutedfrom the originating SIMP’s to their destination IMP’S directly via ground without going through the destination SIMP’S. We will refer to this technique as MASTER. In this scheme, there will benooutstandingpackets in the satellite subnet, and no packet will experience more than one roundtrip propagation delay over the satellite channel. If the ground subnet is not as congested as the satellite subnet, then we not only improve the . overalldelay response,but also ensure thestabilityofthe system. Since MASTER has never been analyzed previously, let us consider thethroughput-delaytradeoffshere.Supposethat the satellite subnet has M SIMP’s. Let h, [packets/s] be the average message ratefrom SIMP u tothe satellite channel,

u = 1,2,

..e,

Of

a/M)

ni

blM)

I

I

I

2

.531

3.059

3‘

.528

4.674

5

,494

5.871

10

489

7.219

M . Th.en the probability q u , that SIMP u attempts in a given time slot, is

qu =-,h U

u = 1,2;-,M

(3)

PSCS

where C, [bitsls] is the capacity of multiaccess satellite channel and 1/11, [bitslpacket] is the packet size as defined earlier. We define random sequences Xu(h) and Y,(h) by

X&)

=

1,

if SIMP u transmits in slot h

0,

otherwise

1,

if SIMP u successfully transmits in slot h

0,

otherwise

and YU@)

=

(5)

for u = 1,2, --,M, and h = 1,2,3, .-. Certainly, X,(h) = 1 if Y u ( h ) = 1 , but not vice versa. If X&) = 1 and Y,(h) = 0 , thentheattempted transmission is afailure due to channel collision. From the definitions of ( 3 ) and (4) it follows that P[X,(h) = 1 3

:=

(6)

qo

and

P[X,(h) = 01 = 1 - qu

6Go

(7)

for u = 1,2, -,M, and all h. Furthermore, by assuming that the inputmessage sequences ‘from different SIMP’s are statistically independent, we readily obtain the following properties for the sequences Y,(h).

P[Yu(h)= 11 = 40

n 47

7 f

I

I

qupu

(8)

u

where Pa represents the probability of success of any attempt transmission from SIMP u. Thethroughput So [packets/slottime]ofthe satellite channel is therefore given by

so =

M

M

P[Y,(h)= 11 = u=l

quPu. u=l

Since the input (or offered) traffic is

HUYNH e t a l . : DESIGN OF MIXED-MEDIA PACKET-SWITCHING NETWORKS

the difference between SIand S o , M

o=l

is the portion of the packet flows that are rerouted via the ground subnet. If we assume that message flows from regional IMP’s to a SIMP can be characterized bya Poisson process, andthat nodal processing delayscan be very small compared with channel queueing delays, then the average delay To [s/packet] experienced byapacket successfully traveling from SIMP u through the satellite channel is given by

where the last term is the average waiting time obtained from an MIDI1queueing model. The overall average packet delay over the satellite channel rS [s/packet] can then be obtained by averaging To’s:

where M

X, =

X,[packets/s] o=l

161 Scheme I and Scheme I1 are the same.Under thepriority schedulingscheme, the IMP’s should be equippedwitha facility to manipulate traffic with two priorityclasses. For a queueing network with general structure, a closedformanalyticsolution has beenobtainedonlyunderthe Markovian assumption:that is, the originationof messages from sources (IMP nodes in our model) should be characterized by Poisson processes, and the service times (message lengths) are independent and identically distributed (iid) with exponentialdistributions.The Poisson assumptionhas been statistically validated in several empirical studies of data traffic (see [14] , [15]). The length of packets in our ground subnet is assumed to be variable witha possible constraintonthe maximum allowable packet size. As long as the coefficient of variation (i.e., the ratio of standard deviation to mean) of the packet size distribution is not far from unity, the exponential assumption should be quite reasonable. However, the length of a packet, once generated at the originating IMP, should remain unchanged throughout the entire transmission over different links within the network; the independence assumption stated above certainly is not realistic in this regard, but it seems that thisassumption is not so critical forthe analysis of such performance measures as throughput and the average delay. It may well be a poor assumption if one is interested in estimating the delay of a particular packet or in the delay distribution rather than just the average value. As for further discussions on these assumptions the reader is referred t o Kleinrock [4] , [ 161 who reports the validation of such a model based on simulation studies. Under the Markovian assumptions madeabove, we can apply the well-known decomposition theorem due to Jackson et al. [18] and [I71anditsrecentextension byBaskett Kobayashiand Reiser [19] . Hence the average delay T, [s/packet] , thata packetexperiences dueto queueing and transmission over the link I, is

is the total input rate to the satellite channel. Note that the condition for the individual queue t o be stable is X, < pSCs, u = 1, 2, ..., M, rather than X, < p,C,. This is because those packets whichrequireretransmissionsare not placed on the satellite channel and rerouted to the ground. For the purposeof this paper (1 3) is all weneed. For further information concerning MASTER, the reader is referred t o a in which XI [packets/s] is the total message flow over link I, CI [bits/s] is the capacity of that link, and l/p [bits/packet] is companion paper by the authors [ 131 . the average length of a packet. A remark is in order concerning (15). This formula holds 111. GROUND SUBNET MODEL notonlyundertheFCFS scheduling rule butundera large The ground subnet is a store-and-forward distributed netclass of disciplines, which are often referred to by the name of “work-conserving’’ queueing disciplines [20] . This class work. In accordance withthetwodifferentoperational schemes of the satellite subnet, we discuss the following two includes the case with two class priority scheduling described cases for the ground subnet model. In Scheme I (i.e., slotted earlier. Furthermore,.it has been shown recently [I91 that in ALOHA), under which the satellite subnet uses slotted order for (15) to apply, the message-routing behavior can be any stochastic or deterministic one, as long as it can be charALOHA without blocking, thegroundsubnet,hasonly acterized by a Markov chain of some order. Furthermore, we originally assigned ground traffic (Le., onlyone type of can assume arbitrary number of different classes, as long as traffic). In Scheme I1 (i.e., MASTER), underwhich SlMP’s their routing behavior is concerned (we still have to assume, divert all retransmissions to the ground net, IMP’s can either however, that all messages are coming fromthecommon addtheseretransmission to their originally assigned packet distribution, which is an exponential distribution of mean 1/p. flows on a first-come, first-served (FCFS) basis, or give these This last property allows us to assume different routing patretransmission packets a higher ,priority, by holding off, but terns depending on the origin of messages. A deterministic withoutpreempting, regular packets flow.Under theFCFS associated with split traffic (bifurcated) routing strategy to be discussed later case, theoperations of thegroundsubnet ’\

L.

162

IEEE TRANSACTIONS ON COMMUNICATIONS, JANUARY 1977

is certainlyaparticular case of general routing behavior to which the simple formula (15) applies. Note that the traffic rates {X,} over the individual links will differ depending on the routing pattern oralgorithm to be chosen.

IV. ROUTING With a mixed-media network the issue of routing is a major concern. With two possible courses to choosefrom-one via satellite and one via ground-the issue is t o choose the set of routes so as t o minimize the overall average network delay. The tradeoffs t o consider are these: the satellite channel has an inherent minimum delay of 0.26 seconds.However,satellite capacity is less costlythan. groundchannel capacityfor medium to long distances, and therefore more satellite capacity is available .at less cost than comparable facilities on the ground.Theground channelsare inherently faster thanthe satellite channel, but because of capacity limitations, are subject to queueing delays, which combined with the store-andforward nodal processing delays, may, in heavy traffic situations, resultin larger overall delays thanthe satellite delays. To ‘summarize, satellitechannels have greaterdelays but also’more cost effectivechannel bandwidth than ground channels. Theroutingprocedure used inthe ARPANET is a distributed adaptive algorithm in which each node has a routing tablewhich is periodically updatedwithminimum distance estimates from its immediate neighbor [6] . In our case study t o follow, we have chosen a deterministic split traffic routing strategy [6] whichbecause it allows traffic to flow on more than one path between a given source-destination node pair, gives a better balance than a fixed routing procedure. We wish t o emphasize, however, thatouranalyticalmodel does not require any specific routing algorithm, but can accommodate any that are static and can be modeled mathematically. Suppose we are given a network of N nodes with a specified topologywhich includesasatellite channel of capacityC, C, [bits/s] (I = 1,2, [bitsls] , a set of ground links capacities *.; L ) , and a demand matrix [yij] ,where yij [packets/s] is the average rate of messages originated at node (IMP) i and destined for node (IMP) j , i,j = 1, 2, -., N. The routing problem is to optimally assign the traffic demand iij’s along different paths of ‘thenetwork so thatthe resulting overall average packet delay is minimized. Note that the link traffic rate X, (1 = 1,2, ..., L ) defined in the preceding section is uniquely . . by the demand matrix [yij], the routing rule, determined retransmission strategy. Let us define the traffic splitting factorgij as the fraction of the traffic, originated at node i and destined for node j , which goes through the ground subnetwork. It is clear that gij = 1 if IMP’S i and j are in the same region. We definegij by

(Sij) of the traffic is first routed to the regional SIMP of IMP i, sent throughthe satellite channeltothe regional SIMP of IMP j , and finally directed to the destination IMP j . Of courses this sequence of steps takes place only when This fraction

the transmission over the satellite channel is successful. If a collision takes place, two different courses of action follow, depending onthe scheme assumed;in case of the ALOHA channel (i.e., Scheme I), the collided packets will attempt retransmission throughthe satellite channel, whereas in the will be MASTER channel (i.e., Scheme II), thesepackets rerouted to the ground subnet. Inboththeslotted ALOHA and MASTER schemes,the overall average delay T for a packet traveling from its origin to destination 1s given’by

where yij = total traffic rate in the network.

y= IJ

Thedefinition of X l and X, and derivations o f the average delay Tl and T , were already, discussed in Sections I1 and 111. In [2 1, appendix 111 we derive the expressions for XI and Xu in terms of { g i j } and {-yij}. Having derived the expression for the overall average packet delay, we can now state formally ourrouting problems as follows: given networkconfiguration,trafficdemandmatrix [yij], and link capacities Cl’s and C, min T

subject t o ( 0 < g i j

< 1, for all ij}.

(1 8)

{gijl

In the system with slotted ALOHA channel (i.e., Scheme I), the average delay T l of those packets sent from SIMP u (u = 1,2, ..., M) over the satellite subnet is equal t o r, of (2),if the traffic demand and routing are such that the input rates from all the SIMP’Sinto the satellite channel are well balanced, I.e.,

Those packets which go through the ground link 1 will experience the average delayof Tl given by (15). Thus the overall average delay of a packet during its entire travel in the net is, from (2),( I 5), and (1 6), and

1

L

X,

T= -- +-Xsrm in Y Y 1=1 Ilc; - hz

Forthe scheme with MASTER channel(Scheme 11) the average delay To forpackets from SIMP u isgiven by (12). The average delay that apacket receives in its transmission over the ground link 1 is given by Tz of (15), irrespective of the scheduling rule chosen. Therefore, by substituting these equations into (16) we obtainthe followingexpression forthe

163

HUYNH e t al. : DESIGN OF MIXED-MEDIA PACKET-SWITCHING NETWORKS

overall delay whicha packetreceives in the net under Scheme 11:

In (21), the traffic rate X, over the ground link I includes not only the originally assigned ground traffic, but also the traffic due t o thosepacketswhich are reroutedfrom SIMP’s after unsuccessful transmissions over the satellite channel. For the class of deterministic and probabilistic routing rules we discussed earlier, we can show that both T of (20) and that of (21) are convex functionsof gij, i, j = 1, 2, -., N. The reason is as follows: as discussed earlier thetraffic rates X, (1 = 1,2, .-, L ) , X, (u = 1,2, -, M), and As are all linear with respect t o gij, and T’s of (20) and (21) are both convex functions with respect t o X,, X, and As. Because of the convexity, the set of { g i j }that minimize T can be found by any optimization procedure. In numerical computations of the case study problems we used Box’s COMPLEX optimization algorithm [22] . This method is a sequential search technique which has proven effective in solving problems with nodinear objective functions subject t o nonlinear inequality constraints. It has an advantage over gradient methods in thatno derivatives are required. It also tends to find the global optimum due to the fact that the initial set of starting points are randomly scattered throughoutthe feasible region.Moreover, its rateof convergence has been shown to be better than Rosenbrock’s algorithm [22]. In [21, appendix 1111 we show the flow chart and give a brief description of this optimization procedure. Example 1: Consider the network with eight nodes (IMP’s) and twenty linksshownin Fig. 3. In this net there are two {5,6,7,8}, regions consisting ofnodes{1,2,3,4}andnodes respectively,and the regional SIMP’s are locatedatnodes1 is assumed to be uniform and 7. The traffic demand matrix with yij = 20 [packets/s] for all i # j and yii = 0 for all i = 1, 2, .*.,8, and the average packet length is assumed t o be 5 12 bits on all ground channels. The packet length on the satellite channel is fixed and equals 1 kbit. The ground link capacities are all assumed to be 50 kbits/s, i.e., C, = 5 X 104 [bits/s] for all 1 = 1, 2, -., 20, and the satellite capacity to be C, = 1.5 X lo6 [bits/s] . The ground subnet routing we used in this example is the split traffic routing (or alternate routing) whichis based on the minimum number of hops required t o transmit packets from a given source node to a destination node. For example, if we want t o send packets from IMP 1 to IMP 8 via the ground net, the minimum number of hops between IMP’s 1 and 8 is four, and there are four alternate paths of four hops: they are path 6 -+ 8; path c) a) 1 + 3 -+ 5 + 7 + 8; path b) 1 3 -+ 5 1 + 3 + 4 -+ 6 8; and path d) 1 + 2 + 4 + 6 + 8. At any node along the paths selected above, if there are two links of the selected paths emanating from the node, then the traffic rate is bifurcated equally on each of. these two links. For instance the traffic coming into IMP 3 will be split into links 8 and 0 equally. Using this ground subnet routing algorithm -+

-+

-+

SATELLITE

?

/ocoiion of m /MP @ /mi& of m /MP ond o S/MP

Fig. 3.

Network model with two SIMP’s and eight IMP’s.

TABLE I1 ROUTING INDEXES FOR TRAFFIC FROM REGION 1 TO REGION 2 for ALOHA

/

&stMtion

1

5

6

7

8

I

1

0

0

0

,855

,681

0

,706

I

0

,315

1

0

1

6

7

0

0

4 1 T= ,229 saccmds

1 . 5 I

onM 2 3 4

1 I

,889 I 1

,995 I

I

,817

T= ,526 seconds

0 ,025 0

.

8

0

,394 ,692 ,805 - 4

we findthatthetraffic assignments between IMP’s 1 and 8 are 1/8 of the total traffic 71.8 over path a), 1/8 over path b), 1/4 over path c), and 1/2 over path d). After obtaining these split factors for each node pair and adding them up appropriately, we obtainthe link traffic X, for each l = 1, 2, -., 20. Because of the symmetry of both the network topology and traffic demand matrix, balanced traffic is maintained throughout the net by use of the ground subnet routing algorithm discussed above. With the above data as input to the routing optimization ALOHA and program, therouting indexes gij forboth MASTER are computed and are given in Table 11. Also shown in Table I1 are the minimum overall average delays of 0.229 seconds for the network using ALOHA and 0.326 seconds for the network using MASTER. ALOHA outperforms MASTER. This is not too surprising; here satellite capacity is much larger than the ground capacities (C, = 1.5 X lo6 bits/s > C,= 5 X 104 bits/s). In addition, the groundcapacities are shared by intraregional traffic. (Recall that gij = 1 if IMP’s i and j reside in the same region.) Thus, the optimum average delay points fallinside the region favoring ALOHA. Attheend of this paper, we showhow this difference can benarrowedbya reassignment of the capacities subject to a fixed linear cost.

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IEEE TRANSACTIONS ON COMMUNICATIONS, JANUARY 1977

In Table 11, only routing indices for traffic from Region 1 t o Region 2 are shown. Because of the symmetry of the network and demand matrix, the routing indices for traffic from Region 2 t o Region 1 are symmetrical t o those from Region 1 t o Region 2. For instance, for networkusing MASTER scheme (lower table),gs2 =gzs = 0.394;g7, =gI8 = 0; etc.

V. CAPACITY ASSIGNMENTS Inthepacket-routingstudies of the previous section we assumed that the ground link capacities and the satellite channel capacity are given. Now we proceed to the capacity assignment problem; that is, we wish t o minimize the, total average message delay T under the total budget constraint. We assume as given the topologyof the network(including SIMP locations), and the demand matrix [yij]. Furthermore we assume, in the present section, that the routing indexes [gij] are given; hence L and the satellite channel the link traffic X I , 1 = 1 , 2 , assumption will be traffic X, are also known. (Thelast removed in Section VI which will discuss the joint optimization problem.) We can formulate the capacityassignment problem as -e.,

L .

minimize T { d , c,

subject to

E bZC1 + b,C, 0 thegroundsubnet (a priori set value), then we judge the minimum pointhas been load, more and more traffic is diverted to.the satellite channel, achieved, and stop the whole procedure. Otherwise go back to and the distinction between MASTER and ALOHA becomes apparent. Since we have assumed a 10 to 1 cost ratio in favor Block 2 and iterate the same cycle. From the above description, we see that each iteration is a of satellite channel, more capacity is assigned to the satellite subnet and less to the ground subnet. As we know, the larger two-stage optimization; in the first stage the set oflink the satellite channelcapacity,thebetter ALOHA 'performs, capacities is fixed, and T is minimized over the set of traffic whereas the smalkr the ground channel capacities, the poorer splitting factors, whereas in the second stage, the set of traffic MASTER performs. Altogether these make ALOHA outpersplitting factors is fixed and T is minimized by the choice of link capacities. Since T is a convex function with respect to form MASTER. Example 3: To further clarify the problem let us consider can be achieved within both C and g, the optimum solution the error determined by E . In fact, for the numerical examples an 8-region network shown in Fig. 6 with same configuration t o follow, with E = 10-5 seconds, each optimum point is ob- as the previous ex.ample, but each node now has an IMP and a 10-20 iterationsdependingonhow close the SIMP. It is a network with 8 IMP'S and 8 SIMP'S. We assume tainedafter

?-'

I

+

167

HUYNH e t a l . : DESIGN OF MIXED-MEDIA PACKET-SWITCHING NETWORKS

:3

1.4-

I

1.2-

es ‘.OP

2-

,0571

, 0 3 6 8

.Os5 .8

7

Fig.

5.

.9

1.0 1.1 1.2 1.3 1.4 115 budget m mdlton un/t costs of ground chonnel copac;ty

Delay-cost tradeoffs for network with eight SIMP’s.

,0368 16

1.7

IMP’s and two

Fig. 7.

Delay-cost tradeoffs for network with eight IMP’S and eight SIMP’s and ten to one cost ratio.

2

SATELLITE

i Fig. 8.

/ocalim of an /MP @ /om?&

Fig. 6 .

of an IMP and o SIMP

Network model with eight IMP’s and eight SIMP’S,

that the demand matrix, meanpacket lengths, and unit-cost ratio remain the same as before. For ALOHA, however,a(M) and ‘ b ( M ) are now estimated to be 0.492 and 6.724, respectively. Results for this network model are depicted in Fig. 7. It is seen that this network model has generally smaller delay than the previous one. This is because of the addition of 6 more S1MP’s.l The network under ALOHA is again superior to that under MASTER,and the difference is more substantial. This is a general trend: as the number of SIMP’s is increased, more traffic goes through the satellite channel, which draws more capacity from the total, and ground subnet gets less of its share.This puts MASTER inadisadvantageousposition relative to ALOHA. For the same network (shown in Fig. 6) Unfortunately, our mathematical model does not include the cost of IMP’S and SIMP’s to reflect this addition. Another way of looking at this problem is: the cost of the SIMP’s has been averaged out and included in the costunit b,; so byretaining the same cost ratio, we essentially assume that the effe.ctive cost of the satellite channel in this example is even lower than that in the previous case.

1.1

1.3

1.5

I7

badget in ml11,on unrr costs of ground chnnel mpnnty

Delay-cost tradeoffs for network with eight IMP’s and eight SIMP’s and three to one cost ratio.

and parameters, if we now reduce the cost ratio to 3 : 1, we obtain different results which are depicted in Fig. 8. As seen in Fig. 8, again, when the budget B > 1 500 000 cost units, no distinction exists between ALOHA and MASTER, but, when B < 1 500 000 cost units, MASTER is slightly better than ALOHA, since now the cost ratio is advantageous for ground subnet, ground channels get more of their share of the total capacity, and excessive capacity in the ground subnet favors MASTER. CONCLUSIONS Inthis paper we have presented some of theimportant design issues for mixed-media packet-switching networks. Satellite packet switching has considerable promise forlowcqst high-bandwidth data communications. However, there is inherent high delay in satellite links which does not appear in groundlinks. Therefore, a mix of thetwocommunication mkdia seems to offer the best of both worlds. In this paper we have examined a number of tradeoffs which offer guidelines for the design and optimum utilization ofmixed-media networks. We have introduced a new communication scheme called multiaccess satellite with terrestrial retransmission

168

IEEE TRANSACTIONS ON COMMUNICATIONS, JANUARY 1977

(MASTER) withthehopethat it would offer significant advantages over slotted ALOHA. Results of this paper show that MASTER does work better than ALOHA under certain circumstances, butnot always so. The capacityassignment, determined by the cost ratio of ground and satellite channels, determines which system is better. Also, the greater sensitivity t o small changes in traffic of ALOHA may make MASTER the better system for many applications. of the two schemes is clearly domThe fact that neither inant suggests that a,mixture of both might be the best system. When a channel collision occurs in such a system, retransmissionscan go either again throughthe satellite subnet, as in ALOHA, with some.probability 6 , or through the ground subnet, as in MASTER, with probability 1 - 6. The probability 6 would be chosen to minimize the average packet delay. This idea will be explored further. In this paper we have not included the cost of IMP’S and SIMP’S in our model. We have also not explored the possibility of sending network control information along the ground and using the satellite for bulk data transmission. Another logical extension of the MASTER scheme will be t o use the satellite channel on a reservation basis, such as suggested by Crowther et al. [23],Roberts[24], and Binder [ 2 5 ] , but use the groundchannelto set up reservations. We plan t o explore these ideas in a subsequent paper. REFERENCES D. L. A. Barber and D.W. Davies, “The NPL data network,” in Proc. Conf. Laboratory Automation, Novosibirsk, U.S.S.R., Oct.1970; also NPLCom. Sci. T.M. 4 7 (NIC14671), Oct. 1970. S. Butterfield, R. Rettberg, and D. Walden, “The satellite IMP for the ARPA network,” in Proc. 7th Hawaii Int. Conf. System Sciences-Subcon. Cornput. Nets, Jan. 1974, pp. 70-73. B.D.Wessler and R. B. Hovey,“Publicpacket-switchednetworks,” Datamation, pp. 85-87, July 1974. L. Kleinrock, CommunicationNets: Stochastic Message Flow and Delay. New York: Dover, 1964. K. D. Felperin,“Interactivetechniques for evaluation of command-control store-and-forward net performance,” Stanford Res. Inst., Stanford,CA, Tech. Note TN-CDS-1, 1969. G. L. Fultz, “Adaptive routing techniques for message switching computer-communications networks,” Ph.D. dissertation, Dep. Comput. Sci., Univ. of California, Los Angeles, available as rep. UCLA-ENG-7252, July 1972. D. G. Cantor and M. Gerla,“Optimal routing in a packetswitched computer network,” IEEE Trans. Comput., vol. C-23, pp. 1062-1069, Oct. 1974. L. Kleinrock and S. S. Lam, “Packet-switching in a slotted satellite channel,” in AFIPS Nut. Comput. Conf. Proc., vol. 42, June 1973, p. 703. S. S. Lam, “Packet-switching in a multi-access broadcast channel with application to satellite communication in a computer network,” Ph.D. dissertation,Dep. Comput. Sci., Univ. of California, Los Angeles, available as rep. UCLA-ENG-7429, Apr. 1974. N. Abramson, “The ALOHA System,” in Colnputer-Communication Networks, N. Abramson and F. F. Kuo, Eds. Englewood Cliffs, NJ: Prentice-Hall, 1973, pp. 501-518. F. F. Kuo and N. Abramson, “Some advances in radio communications for computers,” in Dig. Papers-COMPCON ’73, San Francisco, CA, Feb. 1973, pp. 57-60. L. G. Roberts, “ALOHA packet system with and without slots and capture,” Stanford Res. Inst., Stanford, CA, ARPANET Satellite Syst. Note 8 (NIC 11290), June 1972. D. Huynh, H. Kobayashi,and F. F. Kuo, “Design issues for mixed media packet switching networks,” in Proc. Nut. Comput.

Conj, AFIPS Cwzf. Proc., vol. 45. Montvale, NJ: AFIPS Press, 1976, pp. 541-549. [14] E. Fuchs and P.E. Jackson,“Estimates of distribution of random variables for certain computer communicationstraffic models,” in Proc. ACM Symp. Optimization of Data Communications Systems, Oct. 1969, pp. 202-225. 1151 P. A. W. Lewis and P. C. Yue, “Statistical analysis of series of events in computer systems,” in Sthtistical Computer Performance evaluation, W. Freiberger, Ed. New York: Academic, 1972, pp. 265-280. 1161L. Kleinrock,“Performancemodelsandmeasurements of the ARPA computernetwork,” in Proc. NATO Advanced Study Inst. Computer Communication Networks, R. L. Grimsdale and F. F. Kuo, Eds. Noordhoff International, 1975, pp. 63-88. 1171 J. R. Jackson, “Job shop-like queueingsystems,” Management Science, vol. 10,p. 131, Oct. 1963. [18] F. Baskett, K. M. Chandy, R. R. Muntz, and F. G. Palacios, “Open, closed, and mixed networks of queueswith different classes of customers,” J. Ass. Comput. Mach., vol. 22, pp. 248260, Apr. 1975. [ 191 H. Kobayashi and M. Reiser, “On generalization of job routing behavior in a queueing network model,” IBM Thomas J . Watson Res. Center, Yorktown Heights, NY, res. rep. RC 5679,Oct. 1975. 120) L. Kleinrock, “A conservation law for a wide class of queueing disciplines,” Naval Res.Log. Quart., vol. 12,pp.181-192, 1965. [21] D. Huynh, H. Kobayashi, and F. F. Kuo: “Optimal design of mixed-media packet-switching networks: Routingandcapacity assignment,” IJniv. of Hawaii, Honolulu, ALOHA Syst. Tech. Rep. B76-3, Mar. 1976. [22] M. J . Box, “A new method of constrained optimizationand a comparison with other methods,” Comput. J., p. 42, Aug. 1965. (231 W. Crowther et al., “A systemforbroadcast communications: Reservation A’LOHA,” in Proc. 6th Hawaii Int. Con6 System Sciences, Jan. 1.973, pp. 371-374. [ 241 L. G. Roberts, “Dynamic allocation of satellite capacity through packetreservation,” in AFIPSNut.Comput.Conf. Proc., vol. 42, p. 711, June 1973. 1251 R. Binder, “A dynamic packet switching system for satellite broadcast channels,” Univ. of Hawaii, Honolulu, ALOHA Syst. Tech. Rep. B74-5, Aug. 1974.

* Dieu Huynh (S’76-M’76), for a photographand biography, see this issue, page 157.

* Hisashi Kobayashi (S’66-M’68-SM’76), for aphotographand raphy, see this issue, pages 28-29.

biog-

* Franklin F. Kuo (S’56-M’58-F’72) was born in China in 1934. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Illinois, Urbana, in 1955,1956, and 1958, respectively. He has worked at the General Electric Company, Bell Telephone Laboratories, and Lawrence Radiation Laboratory. He hastaught at the Polytechnic Institute of Brooklyn, the University of Colorado, and was Professor of Electrical Engineering and of Information and Computer Sciences at the University of Hawaii from 1966 to 1975. He was also aconsultanttothe Electronics Engineering Department of the LawrenceRadiationLaboratoryduring 1966-1971.FromJune 1971toSeptember1972,.he was on leave from the University of Hawaii and was a Liaison Scientist with the Office of Naval Research

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-25, NO. 1, JANUARY 1977

in London, England. From September 1972 to December 1975 he was Director, then Technical Director of the ALOHA System, a computer communications research project sponsored by the Defense Advanced Research Projects Agency. The major development of the project was the ALOHANET, a packetbroadcastingradionetworkfor useover ground radio and satellites. He is now Assistant Director (Teleprocessing/ADP) in the Office of the Director of Telecommunicationsand Command and Control Systems,Office of the Secretary of Defense, Washington, D.C. In that capacity he has program management responsibility fcr the new digital data networks, SATIN IV and AUTODIN 11, as well as for the overall World Wide Military Command and Control

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System (WWMCCS) ADP program. He is also the author, coauthor, or coeditor of 6 books and over 40 technical papers. Dr. Kuo was a member (1966-1972) of the COSINE (Computer Sciences in Electrical Enginering) Committee of the National Academy of Engineering. He is Vice Chairman of the ACM Special Interest Group on Data Communications (SIGCOMM), a memberof IFIP Working Group6.1,International Network Working Group (INWG), and a member of the IEEE Communications Society, Computer CommunicationTechnical Committee. He is listed in Who’sWho in America, American Men andWomen of Science,OutstandingEducators of America, and Who’s Who in Engineering.

The Organization of Computer Resources into a Packet Radio Network

Abstract-Packet radio communications provides an effective way to interconnect fixed and mobile computer resources. The ALOHA System at the University of Hawaii first introduced this capability in the context of a single-hop system using off-the-shelf RF equipment with aU terminals within line of sight of the centralstation. The packet radio network described in this paper is I) an extension of the basic Hawaii work to a geographically distributed system involving the use of repeaters to achieve area coverage beyond line of sight, and 2 ) provides added capabilities for authentication, antijam protection, and coexistence with other possibly different systems in the same band. An overview of the packet radio system concept is given in this paper.

INTRODUCTION

I

N this paper, we describe the use of packet radio communication for organizing computer resources into a computer communications network. A system to demonstrate the packet radio concept is being developedby the Advanced Re’search Projects Agency (ARPA). Initial testing in the San Francisco area began in 1975. The attributes of this system are presented and its application to mobile radio communications and computer architecture is briefly discussed. The developmentofpacketswitching has made possible the economic sharing of computer resources [23], [24], [36] over a wide geographic area and, as a valuable byproduct, it has providedaneffectivealternative t o circuitswitchingin providing error-free wide-band communication networks [27] , [30] . The basic architecture of a resource sharing computer network includes Host computers connected to one or more packet switches which may be co-located or remote from the Hosts.Thepacketswitches are interconnected by point-topointdata circuitsaccording t o a topological design which results in low-cost networksfora given target throughput, Manuscript received January 27, 1976. This paper was presented at the National Computer Conference, Anaheim, CA, 1975. The author is with the Advanced Research Projects Agency, Arlington, VA 22209.

reliability, and delay [14] , [29] . For a given packet switching technology,it is possible t o increase networkthroughput greatlyby assembling a higher performanceswitch out of a cluster of lower performance switches (see Fig. 1) and by providing many more circuits between clusters [22] . An alternate approach which uses multiple minicomputerstoobtaina higher performance switch is described in [ 2 11 . The use of packet broadcasting techniques for interconnection becomesattractivewhen the number of minicomputers (ormicroprocessors!) is sufficiently large and the overall traffic flow is small. The use of wire “busses” for packet broadcasting appears certain to be an effective interconn’ection technique. However, packet radio provides another alternative that may be useful for organizing the communications among a large or even a small number of computer resources regardless of the physical setting; inside a box, within a room, or throughout a wide geographic area (see Fig. 2). In addition to its utilityfor mobile communications, packet radio may eventually result in the development of improved techniques for maintenance, breadboarding, and packaging of computer equipment. For a geographically distributed network, economic studies have shown that the cost of local distribution for a large user population can be a significant part of the overall system cost [ l l ] . For this reason alone, it would be desirable to identify more economic techniques for local data distribution than the use of telephone lines. Some progress in thisdirection has already taken place [28]andfurther development of cable systems is expected. However, even if the cost of telephone access lines were notadominantfactor, aneffectivemeans of obtaining mobile access wouldstill be required.This has providedoneincentive for the development of a local radio distribution system. Theburst characteristicsof computer communication [31] will surely be significantly different from the characteristics of mobile radio telephone. By using packet