PACKET DELAY MODELS IN PACKET-SWITCHED NETWORKS: PERFORMANCE ASSESSMENT THROUGH CAPACITY MEASUREMENTS Leopoldo Angrisani Dipartimento di Informatica e Sistemistica Università degli Studi di Napoli “Federico II” Via Claudio 21, 80125 Napoli, Italy E-mail:
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Salvatore D’Antonio C.I.N.I. Consorzio Interuniversitario Nazionale per l’Informatica Via Diocleziano 328 ,80125 Napoli, Italy E-mail:
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Michele Vadursi Dipartimento di Ingegneria Elettrica Università degli Studi di Napoli “Federico II” Via Claudio 21, 80125 Napoli, Italy E-mail:
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Giorgio Ventre Dipartimento di Informatica e Sistemistica Università degli Studi di Napoli “Federico II” Via Claudio 21, 80125 Napoli, Italy E-mail:
[email protected]
KEYWORDS Network Capacity Measurement, Link Bandwidth Measurement, Network Modelling, Packet-Switched Networks. ABSTRACT The paper presents a comparison of the performance of some software tools, mandated to bandwidth measurement in packet-switched networks. The considered tools are based on time measurements, according to specific packet delay models, already presented in the literature and briefly described in the paper. An original measurement station has properly been set up by the authors with the aim of accurately performing the required time measurements, and then utilizing them as inputs for the tools. Final results are reported and compared.
taken with regard to a particular network configuration, details of which are also given. Being the considered tools based on time measurements, the authors have set up a proper measurement station, capable of carrying out the required time measurements by means of a digital counter. This choice allows the tools run with more accurate time estimates; thus, a more reliable comparison can be drawn. THE ONE-PACKET MODEL The One-Packet model predicts the delay experienced by a single packet across a path constituted of n links (Bellowin 1992; Jacobson 1997; Downey 1999; Mah 1999; Lai and Baker 2000). Assumed the packet size is L, the time needed by the packet to reach its destination across n links is n
INTRODUCTION
Tn = ∑ i =1
In order to meet bandwidth requirements of an increasing number of users, the Internet has significantly grown and been enhanced in the last years. As a consequence, the problem of bandwidth measurement, which had already arisen several years ago, is still topical for network monitoring. With regard to a network path constituted of n link, named Bi, i=1,...,n, the link bandwidths, it is possible to define the (end-to-end) capacity, C, as C = min(B1 , B2 , ..., Bn ) (1) Among several software tools for link bandwidths measurement and end-to-end capacity, already presented in the literature, three of them have been selected: (i) clink (Downey 1999); (ii) pchar (Mah 1999) and (iii) Pathrate (Dovrolis et al. 2001). In particular, clink and pchar are based on the one-packet model, while Pathrate is based on the packet-train model. The paper aims at comparing the performance of the aforementioned software tools in terms of measurement repeatability and compatibility. Measurements have been
L + d i + qi Bi
(2)
Equation (2) expresses the packet delay as the sum of the delays accumulated at each link. In particular, L/Bi is the transmission delay of the packet at link i; di is the latency of link i, i.e. the sum of propagation delay and other fixed per-packet delays due to the router; and qi is the queuing delay experienced by the packet at link i. It is worth highlighting some assumptions underlying the model: (i) the transmission delay is assumed to be linear with respect to the packet size; (ii) only store-and-forward routers are present on the path; (iii) links are singlechannel. With regard to the first assumption, it could happen that routers manage their buffers in such a way that the proportionality is not guaranteed. On the contrary, the second assumption is almost always verified on the Internet. The last assumption is more critical. Some links, in fact, consist of multiple channels. In such cases, the application of the one-packet model could lead to wrong bandwidth estimation. As an example, let us suppose a link consists of M channels, each of which has a bandwidth of w bps (bits
per second), so that the overall link bandwidth is M·w bps. Since each packet is routed on a single channel, the bandwidth estimated by means of the one-packet model would be just w, rather than M·w. The presence of cross traffic can be responsible for the queuing delays qi. If the network is probed several times, with packets of the same size, there is a high probability that the minimum value of delay is unaffected by cross traffic, i.e. q1= q2= ...= qn=0. Therefore, by considering the minimum value of delay over several observations for each packet size, the one-packet delay Tn results a linear function of the packet size, i.e. Tn = a n ⋅ L + bn (3) with n 1 = a n ∑B i =1 i n b = d i n ∑ i =1
(4)
Equation (3) is still valid if Tn is the Round-Trip Time (RTT) of a packet from the sender up to link n. In this case, the di terms also include the latencies on the way back and the transmission delay of the acknowledgement from link i, which is constant with respect to L. With the aim of measuring the bandwidth of each link, Variable Packet Size (VPS) techniques probe the network with several packets for different values of L and select the minimum RTT for each considered value of L. A linear regression, performed over these values, provides the value of the slope an. Figure 1 (Lai and Baker 2000) shows how queuing delays due to cross traffic can be filtered out from measurement results. Black dots represent the minimum delay for each probing packet size.
Delay [s]
Packet size [bit]
An estimation of the link bandwidths B1,...,Bn can be achieved recursively. For a one-link path, in fact, B1 = a1-1. For a H-link path (H>1), it is easy to prove that
1 a H − a H −1
When the parameter of interest is the end-to-end capacity of the path (i.e. the bottleneck link bandwidth), rather than the bandwidth of each link, it is useful to refer to a different model, also presented in the literature: the packetpair model (Bolot 1993; Carter and Crovella 1996; Paxson 1997; Dovrolis et al. 2001). The model considers two packets of the same size L, travelling from the same source to the same destination, in the absence of cross traffic along the path. Let us define the dispersion ∆i at the generic link i as the time elapsed from the instant the last bit of the first packet is received at a certain path point to the instant the last bit of the second packet is received at the same point. ∆i can be expressed as
L ∆ i = max , ∆ i −1 Bi
(6)
Equation (6) predicts that if packets do not arrive at link i close enough to queue together (L/BiB1 and let r1 be the average cross traffic incoming rate. The initial train dispersion is ∆0=(N-1)L/B0, while the dispersion at destination, due to the presence of cross traffic, is
∆1 =
different bandwidth values for the connection between the routers: 100 Mbps and 2 Mbps.
B1 B 1 + u1 1 B0
< B1
(10)
Figure 2: Network under test The three tools have been utilized with the aim of measuring the capacity of the path from Host A to Host B. It is worth stressing that, while Pathrate measures the endto-end capacity, pchar and clink measure the link bandwidths. As a consequence, with regard to pchar and clink, the capacity estimation has been achieved by measuring the RTT from Host A to Router 2 (i.e., because of the particular network topology, by setting the initial value of the Time-To-Live field equal to 2). As stated before, considered models (and, consequently, considered software tools) derive an estimation of the bandwidth on the basis of measurements of time. Figure 3 shows the measurement station set up by the authors with the aim of providing software tools with more accurate time measurements.
where u1=r1/B1. It is worth noting that Equations (9) depends on the average amount of cross traffic, but is independent of the distribution of cross traffic packets within the probing train, as well as their exact size. Upon N values’s increasing, the distribution of R becomes unimodal and converges to the ADR. It is also evident that R reduces to the capacity when u1=0, i.e. when there is no cross traffic. Equation (10) can be generalized to the case of a H-hop path (Dovrolis et al. 2001). NETWORK UNDER TEST AND MEASUREMENT STATION In order to carry out the experiments, two couples of hosts have been utilized and a suitable network has been set up. Figure 2 shows the network under test. Host A and Host B are connected to different Fast-Ethernet Local Area Networks (LANs), in particular to two different Cisco 3500 series switches. The switches provide an uplink to two Cisco 2600 series routers (Router 1 and Router 2), which are connected one each other. The performance assessment is based on an extended experimental activity; about a hundred measurements have, in fact, been executed for each configuration. Experiments have been carried out with regard to two
Figure 3: Measurement station The core of the station is a digital counter (HP 53131A). The two channels are connected to, respectively, pin 7 (RTS, Request to Send) and pin 4 (DTR, Data Terminal Ready) of the serial port of one of the hosts. In particular, the counter is connected to the host which performs the time measurements (i.e. the sender for pchar and clink, the receiver for Pathrate). The digital counter provides the value of the time interval between the rising edges of two voltage pulses, which occur, respectively, on channel 1 and channel 2 of the counter. Adequate insertions have been made in the source
codes of the tools in order to generate the two voltage pulses at the right instants. Time estimates attained by means of the described station are then given in input to the tools, and capacity values derived from these measurements are compared. PERFORMANCE COMPARISON Table 1 shows measurement results provided by the tools, for the two considered nominal path capacities (100 Mbps and 2 Mbps). Results are expressed in terms of mean value (µ) and experimental standard deviation (σ); the latter is given in percentage relative terms. Table 1: Measurement results µ [Mbps] clink pchar Pathrate clink Pchar Pathrate
• •
pchar and clink offer similar outcomes, although results provided by the latter presents a slightly greater standard deviation. Results given by VPS techniques (like pcharand clink) have to be corrected, in the presence of store-andforward layer-2 switches. The one packet model, however, remains valid, if hops containing store-andforward switches are modelled as a series of segments (Prasad et al. 2003).
Pathrate clink
σ [%]
Nominal = 100 Mbps 96.50 0.14 95.40 0.17 96.80 0.15 Nominal = 2 Mbps 1.98 0.29 1.98 0.18 1.97 0.17
First of all, it is necessary to highlight that both pchar and clink provide a surprising result when the nominal capacity is 100 Mbps; specifically, estimated capacity is about half the nominal value. As proved by a recent work (Prasad et al. 2003), this is due to the presence of layer-2 store-andforward switches on the network under test, which affects the validity of the model. Specifically, a layer-3 link with a store-and-forward Fast-Ethernet switch inside is equivalent to the series of two layer-2 segments of the same capacity, i.e. to a link of half the nominal capacity. According to these considerations, which definitely apply to our case, measurement results reported in Table 1 have been corrected. The same problem does not arise in the 2 Mbps link, since no switch is present between the routers. Moreover, as Prasad et al. have proved, such an ‘error’ does not propagate on the following links. Figures 4,5 allow a comparison of the results in terms of repeatability and compatibility with regard to, respectively, the 2 Mbps and the 100 Mbps link. The results of each tool are, in fact, expressed in terms of an interval centered at the mean value and whose width is six times the experimental standard deviation (a Gaussian distribution is assumed). It is worth stressing that measurement results are compatible if the related intervals overlap. Repeatability, instead, is strictly connected to the relative experimental standard deviation; the smaller the experimental standard deviation is, the higher the degree of repeatability is. From the analysis of the outcomes, the following considerations can be drawn: • Measurement are compatible, since related intervals overlap for both the nominal capacity values. • The experimental standard deviation is lower than 1% for the all considered tools.
pchar 1,950
1,960
1,970 1,980 bps
1,990
2,000
Figure 4: Measurement Comparison for a Nominal Capacity of 2 Mbps
Pathrate
clink
pchar 95,000 95,500 96,000 96,500 97,000 97,500 bps
Figure 5: Measurement Comparison for a Nominal Capacity of 100 Mbps For the sake of completeness, results provided by the tools, when time estimates are not attained by means of the measurement station, are reported in Table 2. Table 2: Measurement results (II) µ [Mbps] clink pchar Pathrate clink Pchar Pathrate
σ [%]
Nominal = 100 Mbps 89.72 0.86 88.50 0.84 95.95 0.88 Nominal = 2 Mbps 2.01 0.15 1.98 0.11 1.97 0.12
By comparing results reported in the two Tables, it is possible to affirm that when time estimates are not provided by the digital counter, the tools exhibit worse
performance. In particular, the experimental activity shows that: • Measurement results provided by the different tools are not compatible; intervals representing measurement results, in fact, do not overlap. • Differences from nominal values are more marked. This is particularly true for the 100 Mbps link than for the 2 Mbps link. CONCLUSIONS The paper has compared the performance of different packet delay models for packet-switched networks. The performance assessment has been attained through some tools, mandated to bandwidth measurement, which implement the aforementioned models. A suitable measurement station, properly set up by the authors, has been presented, as well. The station provides accurate time estimates, which are then given as inputs to the tools. To sum up some outcomes, provided by the experimental activity, it is possible to affirm that: • Tools based on RTT measurements have proved to be unreliable in presence of layer-2 switches • The adoption of a digital counter to carry out time measurements has clearly turned out to be a winning choice. Measurements, in this case, are evidently more compatible and repeatable; moreover, the difference between nominal and measured values tends to reduce. REFERENCES Bellovin, S.M. 1992. “A Best-Case Network Performance Model” http://www.research.att.com/~smb/papers/netmeas.ps. Bolot, J.C. 1993. “End-to-End Packet Delay and Loss Behavior in the Internet”. In Proceedings of ACM SIGCOMM 1993. Carter, R.L. and M. E. Crovella. 1996. “Measuring Bottleneck Link Speed in Packet-Switched Networks”. Technical Report BU-CS-96-006. Boston University Paxson, V. 1997. “End-to-End Internet Packet Dynamics”. In Proceedings of ACM SIGCOMM 1997. Jacobson, V. 1997. “Pathchar: a Tool to Infer Characteristics of Internet Paths”. ftp://ftp.ee.lbl.gov/pathchar/. Downey, A.B. 1999. “Using pathchar to Estimate Internet Link Characteristics”. In Proceedings of ACM SIGCOMM 1999. Mah, B.A. 1999. “pchar: a Tool for Measuring Internet Path Characteristics”. http://www.employees.org/~bmah/Software/pchar/. Lai, K. and M. Baker. 2000. "Measuring Link Bandwidths Using a Deterministic Model of Packet Delay". In Proceedings of ACM SIGCOMM 2000. Dovrolis, C.; P. Ramanathan; and D. Moore. 2001. “What do packet dispersion techniques measure?”. In Proceedings of IEEE Infocom 2001. pp. 905-914.
Prasad, R.S.; C. Dovrolis; and B. Mah. 2003. “The effect of layer-2 store-and-forward devices on per-hop capacity estimation”. In Proceedings of IEEE Infocom 2003.
AUTHORS’ BIOGRAPHIES LEOPOLDO ANGRISANI was born in Nocera Superiore, SA, Italy, on April 16, 1969. He received the M.S. degree (cum laude) in electronic engineering from the University of Salerno, and the Ph.D. degree in electrical engineering from the University of Napoli Federico II, in 1993 and 1997, respectively. Since 2002 he has been Associate Professor at the Department of “Informatica e Sistemistica” of the University of Napoli Federico II. He is involved in research into new methods based on the wavelet and chirplet transforms for detecting, measuring, and classifying transient signals, new methods based on time-frequency transforms for testing RF equipment for mobile communications, new measurement procedures for communication networks test and measurement, and design, realization, and characterization of VXI instruments based on digital signal processors. GIORGIO VENTRE is Associate Professor of Computer Networks in the Department of Computer Engineering and Systems of the University of Napoli Federico II. He owns a Laurea Degree in Electronic Engineering and a Ph.D. in Computer Engineering, both from University of Napoli Federico II. From 1989 to 1991 he worked at CPS, Center for Research on Parallel Computers of the Italian National Research Council (CNR), doing research in the area of system support for distributed memory computers. From 1991 to 1993 he was with the Tenet Group at the International Computer Science Institute and the University of California at Berkeley, working in the area of Real-Time Protocols for Multimedia Applications. Since 1993 he is back at the University of Napoli Federico II, where is co-leader of the COMICS team. COMICS stands for Computer for Interaction and Communications and is a research initiative in the areas of networking and multimedia communications. Recently Giorgio Ventre has been appointed as Director of ITEM, a research laboratory on multimedia application founded by CINI, the Italian University Consortium for Informatics. ITEM is located in Napoli and hosts a state of the art technological infrastructure in the area of telematics and multimedia systems. As leader of the networking research group at University of Napoli Federico II Giorgio Ventre has been main investigator for a number of national and international research projects, and in particular for BRAIN (EU RACE Programme), NICE, Renaissance, GESTALT (EU ACTS Programme), CADENUS, INTERMON, E-NET (EU IST Programme). Giorgio Ventre has co-authored more than 100 publications: he is member of the IEEE Computer Society and of the ACM. He has served in the Program Committees of international Conferences and Workshops and is reviewer for several international journals and conferences in the area of distributed systems and communication networks.
