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Supporting Network Management with Real-Time. Traffic Models. Prosper Chemouil, Member, IEEE, and Janusz Filipiak, Member, IEEE. Abstract-Real-time ...
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. VOL. 9, NO. 2, FEBRUARY 1991

Supporting Network Management with Real-Time Traffic Models Prosper Chemouil, Member, IEEE, and Janusz Filipiak, Member, IEEE

Abstract-Real-time routing and flow control in circuit-switched networks is investigated. An algorithm is derived which updates routing tables and flow control parameters according to changing load conditions. The network is described by means of stochastic difference equations. A control structure imposed by hardware requirements and realistic network status information patterns is taken into account. It is shown that the global objectives can be achieved by means of shortest route algorithms with state-dependent route lengths. Implementation issues which are related to traffic estimation and prediction are discussed. The performance of a particular algorithm implementation is investigated by simulation.

I. INTRODUCTION

T



HIS paper reports on research made in order to find an efficient state-dependent control of traffic routing and flow control in circuit-switched networks. Presently, problems of traffic management and control in communications networks are a subject of considerable interest. Sophisticated algorithms are implemented in stored program control telephone exchanges to increase profit from the network operation. The analysis and synthesis of traffic management and control in communication networks pose a complex problem. Control rules must be found for a large set of geographically dispersed local controllers acting under stringent time constraints in a random environment. Finding a practical solution requires the cooperation of teletraffic and control engineers to well define the problem. In particular, different implementation issues must be taken into account, which are implied by hardware parameters, quality of network services, and PTT regulations. A survey of dynamic routing techniques for circuit-switched traffic is given in [ 101. Recent implementations are described in [ 11-[3]. There is also extensive literature on modeling and control of dynamic routing. An approach based on learning automata was discussed in [ 141. Static and dynamic flow models are used for a synthesis of control in [ 1 1 1 . Queueing type models are described in [13]. Routing and flow control problems are considered in [6] within the framework of the dynamic flow theory. Currently, routing in a network of trunk groups is done by means of routing tables. For each destination code, the routing table specifies a sequence of overflow directions. Usually, a direct route is tried first. If all trunks on the direct route are busy, alternative routes are attempted in a prespecified order. The sequence of overflow is updated on a time horizon of weeks or months after an analysis of long-term traffic measurements. In contrast to that, the on-line routing control consists of updating

Manuscript received April 17, 1990; revised September 20, 1990. P. Chemouil is with the Centre National d’Etudes des Telecommunications, CNETIPAAIATR, 92 131 Issy-les-Moulineaux, France. J. Filipiak is with the Department of Telecommunications, The University of Mining and Metallurgy, 30-059 Cracow, Poland. IEEE Log Number 9040945.

routing tables with a short cycle length so as to profit from instantaneous traffic fluctuations. A control system is appended to each node which measures the number of busy trunks on all outgoing links and uses that information to determine a sequence of overflow routes, see, e.g., [9]. Practical update times range from several seconds up to several minutes depending on the make of the telephone exchange. Several types of switching machines may coexist in one network, giving a complicated pattern of information on the network state. Our previous research on modeling and control of telephone traffic concentrated on field trials and simulation experiments. Hardware and software elements which we used to test adaptive routing in a real network are described in [9]. We also constructed an analytical model of on-line traffic measurements and used it for time series analysis of sequential traffic records [ 7 ] . Performance of heuristic algorithms was analyzed in [4]. In this paper, we intend to determine a routing rule in a systematic way. An attempt is made to take into account constraints on control impqsed by hardware. The network model is based on realistic patterns of information about the network state. In the subsequent sections, we present link and network models and formulate problems of state-dependent routing. The control problem is solved in Section V . Implementation issues and simulation results are considered in Section VI. Section VI1 concludes results of the paper. 11. NETWORK MODEL

In circuit-switching machines with stored problem control traffic, records are collected by on-line sampling of all trunks going out from an exchange. Since, from the point of view of the switching processor this is a low priority task, the updating period A ? can be large. The update cycle length depends on the type of exchange. The number x ( K ) of trunks busy at time t , are the number U ( K ) of calls accepted in the time period (f,?), are usually recorded. K denotes the measurement epoch. Measurement time instants t, as well as the update cycle length A t can vary from node to node. The following model of traffic measurements on a slightly loaded trunk group was derived in [7]:

,,

K

= 1,

* . .K .

( la)

It was shown that, under an assumption of Poisson arrivals and exponential holding times, coefficients a and b have the following form: a = exp ( - T ) ( Ib)

0733-8716/91/0200-0151$01.OO

b = - [1I

T 0 1991 IEEE

- exp(-T)]

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. VOL. 9, NO. 2, FEBRUARY 1991

152

where Tis the update cycle length normalized by the mean holding time r: T = A r / r . Variable V ( K )can be treated as noise with a zero mean and the variance a:, =

(1 - a2 -

n2)p

Equation (la) written for the link ( j , k ) has the form &(K

+ 1)

= aXJk(K)

forK = 1 , . * K. Denote by a: ( K ) the proposition of traffic entering node j sent to node 1 along the direct link ( j , 1 )

0

4 a;(K)

5 1.

Define next the random routing variable e:, as a proportion of the input traffic U: which is forwarded to the link ( j , k )

e } .

Algorithm I :

(8)

( j ,k) E L ,

(2)

where p denotes the offered traffic measured in E. It is shown in [8], that (la) is valid for loss systems with nonexponential service times. The link model defined by ( 1 ) and (2) is attractive for control applications, We shall use it in the sequel to construct the network model. Denote by N the set of network nodes: N = { i, j , k . . . }, and by L the set of network links: L = { ( i , j ), ( j , k ) * To avoid instabilities [12], we shall admit routes composed of two links at most. This is a common practice in dynamically routed networks. Routing at network nodes is done according to routing tables. Denote by R:, a path from node j to node 1 through node k: R:k = { ( j , k ) , ( k , 1 ) }. The algorithm of updating routing tables consists of the following steps.

+ buJk(K + 1) + Y k ( K + I),

u;k(K

+ 1)

=

ejk(K)

uJ(K+ I),

(j,k)EL,lEN,k # 1

ejk(K)

1

0,

j, k E N

E(.)

=

{Xjk(K),

Ujk(K):

(3)

( j ,k ) E L } .

+

ZJk(K

+ 1)

=

A J k { E ( l ) ,1

=

..'

1

K},

v ( j ,k) EL.

(loa)

and

1) Update the information E ( K ) about the state of all links:

2) Estimate traffic congestion z J k ( ~ 1 ) on link ( j, k ) in the approaching time interval:

(9)

where

j , 1 E N.

Using (9) in (7) and then substituting (7) in (8) gives x,k(K

+ 1)

(4)

3) Determine lengths Q:, [z( K ) ] of routes Rjk, k E N , k # j , from j to 1, for all origin-destination pairsj, 1 E N . 4) For each origin j and destination 1, determine the sequence ( K ) of overflow routes: *;(K)

= {Rjk,,,(K), m =

1

* *

. M:,k,

EN,

k,

#j }

(5)

by arranging them according to their quality. M: denotes the number of admissible overflows. Note that in step 2), the traffic control decision taken at the time instant K takes into account the route congestion during the 1). Different measures ZJk( K ) approaching time interval ( K , K of link congestion can be used for that purpose, as discussed in [7]. The function AJk, which appears in (4),must be chosen accordingly.

+ q k (+~ 1)

for ( j , k )

E

(11)

L.

Calculating averages in the above equations yields

+

111. STATE-DEPENDENT ROUTING Assume that the traffic which enters nodej E N in the interval (t,., t s + l ) from the outside of the network and is destined to 1 ). According to node 1 E N is Poisson with intensity p:( K the definition of traffic intensity

+

Uj(K

1) = Tpj(K

+ I),

j, [€N.

(6)

Under the assumption of Poisson distribution, U:( K ) fully describes U ~ ( K Variables ). r ( ~ l ) = { p : ( ~+ l ) , j , I E N } K = 1 . * K - 1, define the network load pattern. Note that, in this paper, the lower case letters are used to denote deterministic quantities (averages and measurement results). Denote by I( j ) the set of links incoming to nodej: I( j ) = { ( i , j ) : i E N }, and by O( j ) the set of links going out from j : O ( j ) = { ( j , k ) : k E N }. Link ( j , k ) of the route R:k will be called an upstream link, and link ( k , I ) a downstream link. The total traffic offered to the link ( j , k ) is composed of direct, upstream, and downstream traffic

+

(7)

(12) for ( j , k ) E L , where xpy = E [ X p , ] for V ( p . q ) E L and us = E [ U : ] for V r , s E N . Moreover, we have redefined routing eJA(K), variables af on the direct links ( j , k ) : O ~ ? ( K ) : = 1 to stress that all traffic is first forwarded to the direct routes. The control constraints now have the form

+

e:/(K)

1- 1

e:,(%)

2 0,

(13a) ( j ,k ) E

o ( j ) ,k

#

1,

(13b)

for all origin-destination pairs j , 1 E N . IV. INPUTCONTROL Input control procedures limit the amount of traffic admitted to the switching nodes during periods of network failure or traffic overload. Two input control procedures are currently being used: ,a) call gapping, and b) code blocking. In our model, we represent these procedures by means of control variables C ~ J ~ ( K ) ,i , k = 1, . , N . The variable C ~ J ~ ( K defines ) the pro-

153

CHEMOUIL AND FILIPIAK: SUPPORTING NETWORK MANAGEMENT

+

portion of traffic wf ( K 1 ) that is admitted to the network 1. during time epoch K According to this definition

+

+

U ~ ( K

1) = 4 , f ; ( ~W) ~

+ 1)

( K

fori, k E N , i # k

conditions:

(14)

where 0 5

+f

fori, k E N , i # k .

I1

(15)

Substituting (14) in (12) gives the following model: f

( 2oc 1

for ( j , k ) E L . The constraints imposed on the routing variables remain unchanged. Equation (16) can be reformulated so as to represent different flow and congestion control procedures. For instance, dropping destination index k in +:( K ) one applies the same call gapping parameters to all traffic entering node i. Another modification consists of throttling the transit traffic in the same proportion as the fresh traffic. In that case, all terms which appear in curly brackets at the right-hand side of (16) are multiplied by +,( K ) . In the sequel, we use (16). It well represents the selectivity of overload controls and can easily be adapted to different situations.

where f i f ( ~ )denotes the length of the shortest route from j to 1. Basically, the above solution can be implemented using Algorithm l of Section 11. One additional step is needed at which the proportion 1 - +;( K ) of offered traffic is rejected by applying the selective code blocking or call gapping. To fully specify the algorithm steps, we need to decide a form of the objective function. Moreover, the traffic estimation procedure must be made precise. Consider first the form of the function auZ, ( . ). Assume that the network links have finite capacities mur,,tl( U , U ) E L. The routing control consists of uniformly distributing the offered traffic over all links so as to avoid the link saturation, which is equivalent to the minimization of the function aUtj[X,,,(K

V. OPTIMIZATION PROBLE~ Assume that the network performance function Q is separable and does not explicitly depend on 0 ( K ) K-l

+

I)]

[mu,, - X,,,(K

+

(21)

This corresponds to the following form of the route length function for the alternate routes n:k(K)

=

@jk(K)

+

(22a)

mk/(K).

For the direct routes, we obtain

f

=

( 22b )

WJ/(K)’

The link length function is given by

(17) We are interested in the solution of the following problem. Synthesis of a State-Dependent Control: Given the network model defined by (16), (15), and (13), the initial state x ( l ) , andtheloadpattem {wf(K+ l ) : j , EN, K = 2, * . . K } find the routing and input control variables, e j k ( K ) , j , k , 1 E N , and +:( K ) , i , k E N , such that the index Q defined by (17) takes on the minimun value. The following theorem defines the shortest route property of optimum solution to the above problem. The proof is given in the Appendix. Theorem: Routes Rjk, which are used by the traffic from origin j to destination 1, have the same length

u,,,(K)

= x,,,(x

and may be interpreted as the state-dependent link length. The input control variables +;( K ) are determined by the following

1) - mu,,,

V(U, U )

EL.

(23)

In the above formulas, we have dropped the coeffident A / ( 1 - a ) that does not affect the route classification. That coefficient cannot be omitted, however, in the case of input control. Consider the following form of the function S,,,(. ):

sJ/[@j(K)]

=

[’ - +j(K)]2’

(24)

The minimization of that function corresponds to fair throttling of traffic at all nodes. Substituting (24) in (20a) gives b

1

- +;(K)

and 0