Fairness in DQDB Revisited: A New Solution∗

Kurt Maly† Stephan Olariu† Liping Zhang† Nageswara Rao‡

November 5, 2002

Abstract

The DQDB (Distributed Queue Dual Bus) system consists of a linear arrangementof nodes that communicate with each other using two contra-flowing buses; the nodesuse an extremely simple protocol to send messages on these buses. This simple andelegant protocol has been found to be very challenging to analyze. It has been longrecognized that DQDB suffers from inherent access unfairness problems and severalsolutions to this problem have been proposed in the literature. Unfortunately, noneof these solutions is completely satisfactory. The main contribution of this work is toa new way of looking at fairness in a DQDB system. Our scheme is very simple andefficient to implement and compares favorably with the leading rate-controlled schemesproposed in the literature. In addition, simulation results show that in the presence ofnon-uniform loads, such as a file server being brought up, our scheme converges rapidlyto a fair steady state.

Keywords and Phases: network protocols, fairness, slotted networks, DQDB.

1 Introduction

High speed Metropolitan Area Networks (MAN) are presently being developed to accom-modate the increasing demand for higher transmission speeds over large geographical ar-eas. In addition, the functional requirements of a MAN network call for supporting in-tegrated traffic services, namely data, voice, and compressed video. Towards achievingthese objectives, two major MAN architectures have been recently studied: (1) the ANSIX3T9.5 FDDI ring [1] and (2) the IEEE 802.6 dualbus [2, 20]. The latter, called DistributedQueue Dual Bus (DQDB) has been adopted by the IEEE 802.6 as the standard protocol forMetropolitan Area Networks [2, 24]. An account of the evolution of DQDB is presented in[27]. DQDB is a totally distributed and contention-free protocol. Several researchers haveanalyzed the behavior of the protocol from the performance and fairness points of view[3, 4, 5, 6, 7, 8, 9, 12, 15, 16, 19, 21, 25, 28, 31]. Early simulation results [28, 29, 33, 34, 35]have demonstrated the theoretical feasibility of delivering high speed data service like radi-ological images by using DQDB technology. In [28, 29] it is argued that DQDB is superior∗Work supported in part by NASA grant #187264, by NSF grants CCR-9407180 and CCR-9522098, and

by ONR grant N00014-97-1-0526.†Department of Computer Science, Old Dominion University, Norfolk, VA 23529-0162‡Center for Engineering Systems Advanced Research, Oak Ridge National Laboratory, Oak Ridge, TN

37831-6364

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to FDDI over a wide range of network parameters. For a comprehensive and very readableoverview of the DQDB literature the reader is referred to the excellent survey of Mukherjeeand Biskidian [22].

There seems to be a general consensus that the DQDB system has rather severe problemsof fairness [6, 10, 13, 14, 15, 18, 19, 25, 30]. These fairness problems have been demonstratedby analytical analyses [8, 7, 11, 15, 19, 25] and have also been confirmed in a number of welldocumented simulations [6, 8, 11, 14, 18]. Among others, the authors [19, 25] have provenanalytically that DQDB is unfair at all load levels.

Given the simplicity and elegance of DQDB a number of solutions to the unfairnessproblem have been proposed during the years, each of them modifying the standard DQDBprotocol in an effort to stamp out what was perceived to be the cause of the unfair behavior[13, 14, 21, 23, 26, 29, 32]. For example, Myles [23] and Wainwright and Myles [29] proposeda relatively simple modification of the DQDB protocol. Their idea is to avoid unnecessaryrequests to be transmitted on the request bus when an active node receives a request signalfrom downstream nodes. To keep the correct operation of the protocol, only the value ofthe request counter is incremented. Unfortunately, as pointed out by Fdida and Santoso [9]this modification does not work well on large networks. Yet another solution was proposedin [19] for load to medium loads. Their method involved a simple dynamic compensationscheme which consists of a mechanism whereby certain nodes relinquish slots on the buswhich, otherwise, they could have used to send messages. However, the solution of [19]leaves unanswered the high-load situations that are typical of most practical settings.

More recently, Hahne et al. [13] have proposed a way of addressing the unfairnessproblem of DQDB. Their solution, although imperfect, seems to be widely accepted as themost suitable compromise and has been incorporated in a newer version (October 1989) ofthe DQDB protocol. This has been referred to, and known in the literature, as the latestDQDB (see also [9]). In essence, the solution proposed in [13] can be implemented byadding a “trigger” counter to the existing ones (described in Section 2) and incrementingthis trigger counter by 1 every time a node transmits a data segment. Whenever the triggercounter reaches a certain value, it is decremented by a certain quantity and the requestcounter is automatically incremented by one.

The main contribution of this paper is to propose a new approach to deal with thefairness problem in DQDB. Our solution is based on a concept of fairness different from allthe proposed solutions. In essence, our point is that in a fair system it is desirable to makewait time as even as possible among nodes. We feel that this criterion for fairness is morerealistic in local and metropolitan area networks. We introduce a scheme which implementsour definition of fairness with minimal effort. We show that the cost in low-to-medium loadsituations is null and relatively low at overload. In realistic situations, the network featuresnon-uniform loads due, in part, to large file transfers being performed: file servers are acase in point. It is important to assess how long it takes for the system to reach a steadystate after such a perturbation occurs. Our simulation results show that in the presence ofnon-uniform loads, our proposed scheme converges rapidly to a fair steady state.

The paper is organized as follows: in Section 2 we present an overview of DQDB; in Sec-tion 3 we discuss the notion of fairness in a network; in Section 4 we give an implementationof our wait-time fairness; Section 5 contains simulation results; finally, Section 6 contains asummary along with directions for further research.

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2 The DQDB System – an Overview

In this section, we present a brief overview of the DQDB system. For a more detaileddiscussion of this system the reader is referred to [2, 9, 22]. DQDB features a dual bustopology resembling that of Fasnet [17]. The two buses support communication in oppositedirections allowing full duplex communication between any pair of nodes on the network.The n nodes are connected to both buses and the communication is made on the appropriatebus, as illustrated in Figure 1. DQDB is a slotted system: the slots are generated at thebeginning of each bus and are sent down the buses at a constant rate for each bus. It hasbeen argued [13] that as transmission rates and distances spanned by the network increase,slotted networks tend to be more efficient that token-passing systems.

In principle, in a slotted system, a node with data to transmit will acquire the firstempty slot on the desired bus. The problem with this simple-minded approach is thatnode located closer to the slot generator could acquire all the slots preventing others fromtransmitting. This becomes a significant problem at high loads. The major contribution ofDQDB is that it uses the reverse bus for the purpose of reserving slots on the desired bus.In DQDB each slot contains a busy bit and a request bit (see [9] for a detailed discussion).The busy bit makes it easy to determine whether the slot is in use or not, that is, if anothernode has already inserted a message in the slot. The request bit on the reverse bus is usedto notify nodes lying upstream on the desired bus that a node has a message to send. Inthis scheme, a node that wants to transmit on one bus will send a request bit on the reversebus and waits for an unused slot to arrive on the desired bus.

To implement this scheme in DQDB, each node maintains dedicated counters for eachof the contra flowing unidirectional buses. The Request Counter keeps track of the numberof unserved requests from downstream nodes. Nodes with no messages to transmit willdecrement the Request Counter by one (provided it is not zero) for each empty slot passingon that bus. In contrast to this, the Request Counter is incremented by one for each request

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detected on the reverse bus. This way, each node keeps a current state record which holdsthe number of nodes waiting for access downstream on the bus. Any node wishing to send amessage on a specific bus writes into the next free Request Bit on the reverse bus. Further,it transfers the current value of the Request Counter into a Countdown Counter. ThisCountdown Counter indicates the number of requests for access to this specific bus whichhave to be satisfied before the segment at current node may be sent, and is decremented byone for each empty slot detected. In this state, the Request Counter continues to registerthe requests on the reverse bus. When the Countdown Counter reaches zero, the segmentis written into the next empty slot.

It should be noted that the operations of writing requests and sending segments areindependent. That is, the access for segments is not inhibited if the value of the CountdownCounter is zero but the request associated with the segment has not yet been written ontothe reverse bus. As mentioned before, this rather interesting protocol does not guaranteefair access to the nodes in terms of the expected delay time for a job at a node. In fact,both analytic analyses and simulation results have shown that this protocol is inherentlyunfair in that it does not guarantee fairness at any load [9, 13, 19, 22, 21, 25].

3 Fairness in a communication network

In [13] the word fair is used to describe situations (i.e. networks, protocols, and loadingconditions) where the relative throughputs (or delays) of competing network users are inroughly the same proportions as they would if those same users with the same loads wereusing the DQDB protocol over a very short bus. The key to the technique proposed in [13]to address the fairness problem of DQDB is the concept of rate-controlled fairness: everynode is limited to send at the rate of at most R on each bus where R is such that anynode with an offered rate γ below R can send at the rate γ, while all others will send atthe rate R. (Here, all rates are measured in segments/slot time.) Letting δi stand for therate-controlled traffic of node i (1 ≤ i ≤ n), the theoretical throughput of the system isdenoted by T (R) and satisfies

T (R) =n∑i=1

δi = 1. (1)

We note that the theoretical throughput bound spell out in equation 1 is, in generalunattainable due to the bandwidth overhead needed for control. Nonetheless, to make theanalysis more tractable, in the sequel of this paper, we shall assume that equation 1 holds.For the purpose of computing the theoretical control rate R, we shall assume a uniform loadon the two buses. More precisely, messages to be transmitted arrive at nodes according to aPoisson arrival process with a rate of λ at full load. In addition, the slots are assumed to begenerated at a constant rate of n×λ for each bus. For simplicity, we assume that messagesand slots have the same length. We further assume that a message arriving at node i(1 ≤ i ≤ n) is destined to any other node according to a uniform probability distribution.The (average) load of the network is denoted by f . At load f we assume that at each nodemessages arrive at a rate of λf .

Consider the bus on which traffic moves from node 1 to node n. Our assumption aboutmessages being destined uniformly to any other node guarantees that, on this bus, the

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offered load at node i is li = (n−i)λfn−1 , and that the total offered load on the bus is given by

T1 =n∑i=1

(n− i)λfn− 1

=λf

n− 1

n∑i=1

(n− i) =λf

n− 1

n−1∑j=0

j =λfn

2(2)

which is exactly half of the load on the two buses, as it should.If λfn

2 is larger than 1, then we would like to optimally rate-control the process. Specif-ically, we want to compute a value for i such that nodes 1, 2, ..., i will have a controlledrate of R = (n−i)λf

n−1 , while the remaining n − i nodes, will send at their original rate. Thetheoretical throughput, therefore, can be expressed as

T (R) = i(n− i)λfn− 1

+n∑

j=i+1

(n− i)λfn− 1

= 1. (3)

Writing∑nj=i+1

(n−i)λfn−1 = λf

n−1(∑nj=1(n− j)−

∑ij=1(n− j)) = λf

n−1(∑n−1k=0 k − n− i+

∑ij=1 j)

= λfn−1

(n(n−1)

2 − ni+ i(i+1)2

),

(3) becomes

T (R) = λfn−1

(n(n−1)

2 − i(i−1)2

).

Solving for i yields

i =1 +

√1 + 4n(n− 1)− 8(n−1)

λf

2. (4)

Note that, in general, the value of i determined by (4) is not an integer and, consequently,the optimal theoretical rate R cannot always be attained. However, it turns out that thevalue of i returned by (4) and rounded appropriately is a very good approximation of thetheoretical rate. To compute the value of R, we let ∆ stand for

√1 + 4n(n− 1)− 8(n−1)

λf .With this, we can write

R = λf − λf2(n−1)(∆− 1)

which is the desired value of the control rate.Clearly, the rate R satisfying (1) is a theoretical value which may or may not be possible

to compute in practice. For this reason, instead of computing R, an approximation R′

(actually, in [13] this is also referred to as R) is proposed in [13] where it is argued that R′

should be proportional to the idle bus capacity. With ρi and γi standing for the offered andcarried load at node i, respectively, we can write

R′ = β ∗ (1−n∑i=1

γi), and γi = min{R′, ρi}. (5)

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Here, β > 1 is a proportionality factor. Furthermore, several examples in [13] suggest thata good value for β is around 9. In this context we shall define the real throughput of thesystem by

T (R′) =n∑i=1

γi. (6)

with the γi’s computed in (5).Clearly, the real throughput is suboptimal and, consequently, we define the bandwidth

wastage as a function of β as follows

w(β) =| T (R)− T (R′) | . (7)

Notice that as long as the total offered load∑ni=1 ρi does not exceed 1, that is, the network

is not overloaded, there is no need for rate control. Consequently, our definition of wastagein (7) implies that bandwidth is wasted only in an overload situation.

Figure 2 shows how the amount of bandwidth wastage depends on the value of β. Forthe purpose of our simulation, we consider a network with 50 nodes, destination addressesuniformly distributed, and a load offered at 100% uniformly on the two buses. The offeredload used here is offered data traffic. To obtain bus traffic the overhead of 24 bits for every288 bits has still to be added.

In the remainder of the paper the value of β = 9 is assumed. Calculating the theoreticalrate R satisfying (1) gives the ideal fairness distribution and R′, the real rate, is the bestvalue we could find by simulation as described in the latest DQDB.

We propose a simple and natural concept of fairness that we shall refer to as wait-timefairness. The basic idea of wait-time fairness is to have each message have the same expected

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delay. The wait-time oriented fairness scheme allows some nodes to take more than theirfair share of bandwidth. This seems to be appropriate as in modern networks we do havespecial nodes such a file servers, bridges and gateways which need more than their fair share.It would certainly be counter-productive to control the file server while letting everybodyelse transmit at their full load.

4 Implementation of Wait-Time fairness

Recall that in standard DQDB when a node receives a message for transmission, the RequestCounter is transferred to the Countdown Counter, which will now contain the number ofunsatisfied requests from downstream nodes that have to be satisfied before the node’sown queued segment can be transmitted. If in the meantime another message arrives noparticular action is taken until this new message is ready for transmission. At overload,queues will build up at nodes, and as this happens DQDB loses track of the orderinginteraction between messages at different nodes. For all practical purpose, this results inthe ordering of messages being lost: the net effect translates into an unfair situation acrossthe network.

We propose to remedy this with a simple solution. Whenever a message arrives at a nodewe propose to record the contents of the Request Counter in the message’s own CountdownCounter and to reset the Request Counter to zero. Simulation results show that our schemebetter captures the inherent ordering among messages received at nodes, resulting in a faireroverall behavior of the network.

The impact of our scheme is even better seen in the more realistic case where the messagesize does not equal the slot size. Indeed, the point is made by several authors [9, 13] thatunfairness occurs in the presence of large messages arriving for transmission. As DQDBbreaks messages up into segments, our scheme guarantees that the first segment of themessage will have in its Countdown Counter the current value of the Request Counter.Since all the segments of the message are considered to arrive at the same time, subsequentsegments will have a Countdown Counter containing zero, that is the correct value of theRequest Counter.

In addition, it is worth noting that in the absence of overload, implementing our schemecosts nothing at all. At overload, the only cost is to record the number of messages whoseCountdown Counter receives the value of zero, as described above.

5 Simulation results

The simulation model we developed is based on the discrete event simulation view and iswritten in Simscript. Because simulation runs tend to be lengthy, we have modeled onlyone bus at 150 Mb/s and extrapolated the results to the two-bus system by taking weightedaverages.

In the validation phase we calculated the metrics discussed below for each subintervalof 50 ms of simulation time as well as for the entire simulation. Using a 90% confidencethreshold we stopped the simulation when the confidence interval was smaller than 10% ofthe metrics calculated for the entire simulation time and the metric value was within the

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interval. We determined this time for a variety of parameter choices and established that inall stable network situations two seconds of simulation time was enough to meet the abovecriterion. We ran each case with up to five different random number streams and when runfor the proper time obtained results within less than 5% of each other.

We studied various parameters such as network length, message size, and offered loadand metrics ranging from throughput, wait time, response time and service time. For thepurpose of this paper we have selected the case of a 50 km network with 50 equally spacednodes. It is worth noting that since DQDB adds 24 bits to every segment sent, of 100%bus capacity only 92.3% is actually used to transmit data. In all our figures, therefore, thethroughput is to be interpreted as real data throughput, that is, 92.3% of the total buscapacity.

Figure 3 depicts the results of the rate-controlled fairness concept applied to DQDBwith the same assumptions as above. The scale in Figure 3 is chosen to have∑n

i=1 li = load

where load = 1.00 in the case shown. In terms of throughput, Figure 3 and Figure 4 showthe difference between the two approaches to fairness.

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Perhaps more startling is the difference if we consider wait time instead of throughput.Although at the offered load wait time is unbounded we can compare two different schemesat the same time point. Figure 5 shows the typical behavior of wait time of latest DQDBat overload and what could be expected from a wait-time fairness scheme. Note that the

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straight line corresponds to the optimal value of R.Next, we show the difference between the two schemes in the presence of non-uniform

loads in the network. We have simulated the behavior of the rate-controlled fairness schemeand the wait-time fairness scheme in the more realistic situation where some nodes performlarge file transfers. This is a typical situation occurring, for example, when a file server isbrought up. Clearly, it would be counter-productive to control the file server while lettingeverybody else transmit at their full load. In fact, that appears to be exactly what the rate-controlled fairness does! To illustrate the difference between the two schemes we assumedone file server having 25% of the traffic and the other 49 nodes having 75% of the traffic.Notice that because of the way the rate-controlled fairness scheme works, the file servercannot deliver the desired amount of data on the bus, being limited, as all other nodes to acertain maximum quota. On the other hand, in the wait-time fairness scheme the file servercan deliver more information on the bus resulting in what we would refer to as wait-timefairness on the network.

The simulation results are summarized by Figure 6 presented below.

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To see how fast our scheme converges to a fair steady state in the presence of non-uniform traffic a file server is simulated at node 13; specifically, at initial time we assumea steady state situation with a uniform load of 90%. After 0.2 seconds we bring up a fileserver at node 13, resulting in 10% extra load at this node. Figures 7 and 8 show how therate-controlled and our own scheme cope with the situation.

Next, we present simulation results corresponding to the general case where the message-size equals k * segment-size. For definiteness, we consider the cases k = 2, k = 4, and k = 8.Our findings are summarized in Figures 9, 10, 11, and 12. More precisely, Figures 9 and10 present wait time and throughput for latest DQDB, while Figures 11, and 12 present

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the wait time and throughput for our fairness scheme. Again, a uniform load of 100% isassumed.

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Further, it is interesting to compare the performance of the two fairness schemes whenit comes to the throughput and wait time (delays) on the two buses combined. This time,we shall consider, again, that the message size equals the segment size. The results of oursimulation are featured in Figures 13 and 14.

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6 Concluding remarks and further work

It has been recognized by several researchers that standard DQDB is inherently unfairregardless of the load on the system. To address the problem Hahne et al. [13] haveproposed a fairness scheme based on a certain control rate imposed upon nodes that tendto use more than their fair share of bandwidth. In this paper we proposed a new solutionto the unfairness problem of DQDB, based on a concept of fairness different from [13].

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In essence our point is that in a fair system it is desirable to make wait time as even aspossible among nodes. We feel that this criterion for fairness is more realistic in local andmetropolitan area networks. We introduced a scheme which implements our definition offairness with minimal effort. We showed that the cost in low-to-medium load situations isnull and relatively low at overload.

More work remains to be done, however. To begin, the problem of non-uniform loadsituations from node to node have to be addressed. This corresponds to the (more) real-istic case where there are two or more file servers on a network. An interesting idea forfurther research is to compute the values of β in (2) dynamically, having the network adjustautomatically to changes in load. We feel that this is a very promising area for furtherinvestigation.

Acknowledgements: The authors wish to thank four anonymous referes for their con-structive comments that that enhanced the readability of the manuscript.

References

[1] American National Standard, Fiber Distributed Data Interface (FDDI) token ring me-dia access control, ANSI X3.139-1987, November 5, 1987.

[2] Proposed Standard: DQDB Metropolitan Area Network, P.802.6 /D9, Draft - Pub-lished for IEEE, August 7, 1989.

[3] C. Bisdikian, Waiting time analysis in a single buffer DQDB (802.6) Network, IEEEJournal on Selected Areas in Communications, 8 (1990), 1565–1573.

[4] C. Bisdikian, A queuing model with applications to bridges and the DQDB (IEEE802.6) MAN, Computer Networks and ISDN Systems, 25 (1993) 1279–1289.

[5] C. Y. R. Chen, G. A. Makhoul, and D. S. Meliksetian, A queuing analysis of theperformance of DQDB, IEEE/ACM Transactions on Networking, 3, (1995), 872–881.

[6] M. Conti, E. Gregory, and L. Lenzini, DQDB Media Access Control Protocol: Perfor-mance Evaluation and Unfairness Analysis, Proc. 3rd IEEE Workshop on MetropolitanArea Networks, 1989, 7.3.1-7.3.33.

[7] P. Davids, P. Martini, Performance analysis of DQDB, 9th Annual InternationalPhoenix Conference on Computers and Communications, Scottsdale, Arizona, March1990, 548–555.

[8] P. Davids, T. Welzel, Performance analysis of DQDB based on simulation, Proc. 3rdIEEE Workshop on Metropolitan Area Networks, 1989, 7.6.1-7.6.15.

[9] S. Fdida, H. Santoso, Performance issues of DQDB, 4th International Conference onData Communication Systems and Their Performance, Barcelona, June 20-22, 1990.

[10] S. Fdida, H. Santoso, Approximate performance model and fairness condition of theDQDB protocol, NATO Advanced Research Workshop on Architecture and Perfor-mance Issues of High-Capacity LANs and MANs, Sophia Antipolis, France, June 1990.

15

[11] M. W. Garrett and S-Q Li, A Study of Slot Reuse in Dual Bus Multiple Access Net-works, Proc. IEEE INFOCOM ’90, 617–629.

[12] P. T. Gia and T. Stock, Approximate analysis of the DQDB access protocol, ComputerNetworks and ISDN Systems, 20 (1990) 231–240.

[13] E. L. Hahne, A. K. Choudhury, and N. F. Maxemchuk, Improving the fairness ofDistributed-Queue-Dual-Bus Networks, Proc. IEEE INFOCOM ’90, 175–184.

[14] E. Y. Huang, L. F. Merakos, On the access fairness of the DQDB MAN protocol, 9thAnnual International Phoenix Conference on Computers and Communications, March1990, Scottsdale, Arizona, 556–559.

[15] H. Kaur and G. Campbell, DQDB - An access delay analysis, Proc. IEEE INFOCOM’90, 630–635.

[16] L. N. Kumar and C. Douligeris, Demand and service matching at heavy loads: adynamic bandwidth control mechanism for DQDM MAN’s, IEEE Transactions onCommunications, 44, (1996), 1485–1495.

[17] J. O. Limb and C. Flores, Description of Fasnet - A unidirectional local area commu-nication network, BSTJ, 61, (1992), 1413–1440.

[18] A. Lombardo, S. Palazzo, D. Panno, R. Pingnatelli, and L. Susanna, An adaptive policymechanism for a DQDB MAN, Computer Networks and ISDN Systems, 25 (1993) 1119–1126.

[19] K. Maly, N. Rao, S. Olariu, L. Zhang, and D. Game, Average waiting time and fairnessstudies in DQDB, Proc. International Conf. on Parallel Processing, St. Charles, Illinois,1991, II, 278–279.

[20] J. F. Mollenauer, Standards for metropolitan area networks, IEEE CommunicationsMagazine, 26 (1988), 15–19.

[21] B. Mukherjee and S. Banerjee, Alternative strategies for improving fairness in an ana-lytical model of the DQDB network, IEEE Transactions on Computers, C-42, (1993),151–167.

[22] B. Mukherjee and C. Biskidian, A journey through the DQDB network literature,Performance Evaluation, 16 (1992) 129–158.

[23] A. Myles, DQDB simulation and MAC protocol analysis, Electronic Letters, 25, (1989),616–618.

[24] R.M. Newman, Z.L. Budrikis, J.L. Hullett, The QPSX man, IEEE CommunicationsMagazine, 26, (1988), 20–28.

[25] N. Rao, K. Maly, S. Olariu, L. Zhang, and D. Game, Average waiting time profiles ofUniform DQDB, IEEE Transactions on Parallel and Distributed Systems, 6, (1995),1068–1084. A preliminary version appeared in Proc. IEEE INFOCOM, Toronto, On-tario, June 1994, 1326–1336.

16

[26] M. A. Rodriguez, Erasure node: Performance Improvements for the IEEE 802.6 MAN,Proc. IEEE INFOCOM ’91, 636–643.

[27] K. Sauer and W. Schodl, performance aspects of the DQDB protocol, Computer Net-works and ISDN Systems, 20 (1990) 253–260.

[28] R. Vallee, L. O. Barbosa, and N. D. Georganas, Interconnection of Token Rings byIEEE 802.6 Metropolitan Area Networks, Proc. IEEE INFOCOM ’89, Ottawa.

[29] N. Wainwright and A. Myles, A comparison of the Delay Characteristics of the FDDIand IEEE 802.6 MAC Layer Protocols, Hewlett Packard Laboratories, InformationSystem Center, March 1989.

[30] J.W. Wong, Throughput of DQDB Networks under Heavy Load, Proc. 7th EuropeanFiber Optic Communications & Local Area Networks Exposition EFOC LAN, 1989,146–151.

[31] C.-S. Wu, N.-F. Huang and G.-K. Ma, A dual bus approach for LAN interworking withATM networks, ACM Computer Communication Review, 25, (1995), 66–85.

[32] T. Yokotani, H. Sato, and S. Nakatsuka, A study of performance improvement algo-rithm in DQDB MAN, Computer Networks and ISDN Systems, 25 (1993) 1107–1117.

[33] M. Zuckerman, On packet switching capacity in QPSX, Proc. of IEEE/IEICE GlobalTelecommunications Conf. GLOBECOM’87, Tokyo, Japan, 1987, 45.2.1-45.2.5.

[34] M. Zuckerman, Queuing performance of QPSX, Proc. of the 12th International Tele-traffic Congress ITC 12, Torino, Italy, 1988, 2.2B.6.1-2.2B.6.7.

[35] M. Zuckerman, Overload Control of Isochronous Traffic in QPSX, Proc. of IEEE GlobalTelecommunications Conf GLOBECOM’88, Hollywood, Florida, 1988, 38.3.1.-38.3.5.

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