packet loss performance of selective cell discard schemes in atm switches

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 15, NO. 5, JUNE 1997 903

Packet Loss Performance of SelectiveCell Discard Schemes in ATM Switches

Kenji Kawahara, Koichiro Kitajima, Tetsuya Takine,Member, IEEE, and Yuji Oie,Member, IEEE

Abstract—In transport-layer protocols such as TCP over ATMnetworks, a packet is discarded when one or more cells ofthat packet are lost, and the destination node then requires itssource to retransmit the corrupted packet. Therefore, once oneof the cells constituting a packet is lost, its subsequent cells ofthe corrupted packet waste network resources. Thus, discardingthose cells will enable us to efficiently utilize network resources,and will improve the packet loss probability. In this paper, wefocus on tail dropping (TD) and early packet discard (EPD)as selective cell discard schemes which enforce the switches todiscard some of the arriving cells instead of relaying them. Weexactly analyze the packet loss probability in a system applyingthese schemes. Their advantages and limits are then discussedbased on numerical results derived through the analysis.

Index Terms—ATM, early packet discard, perforamance anal-ysis, selective cell discard, tail dropping.

I. INTRODUCTION

T HE asynchronous transfer mode (ATM) has been adoptedas a way to accommodate various traffic from multimedia

in B-ISDN. In ATM networks, user information is transmittedon cells that consist of 48-byte payload and 5-byte header.On the other hand, the transport-layer located above the ATMlayer handles the transmission based on packets; each packetis composed of one or more cells. The function of the transportlayer is to manage end-to-end communication, and to performerror control and traffic control using packets. If a cell islost within the network, the destination cannot reassemble thepacket to which the cell belonged, and requires the sourceto retransmit the packet. Therefore, once one of the cellsconstituting a packet is lost, its subsequent cells in the packetare not worth relaying within the network. Thus, the networkresources could be utilized efficiently in a way to selectivelydiscard such cells at the multiplexing node or the ATM switch[1]–[4].

The ATM adaptation layer (AAL), which is the upper layerof the ATM, transforms a packet received from the transportlayer into cells at the source node and vice versa at thedestination node. AAL5, one of the AAL protocols, appends

Manuscript received May 1, 1996; revised December 1, 1996.K. Kawahara and Y. Oie are with the Department of Computer Science and

Electronics, Faculty of Computer Science and Systems Engineering, KyushuInstitute of Technology, Iizuka 820, Japan.

K. Kitajima is with the Network Product Business Department, Fuji XeroxCompany, Ltd, Minato-ku, Tokyo 107, Japan.

T. Takine is with the Department of Information Systems Engineering,Faculty of Engineering, Osaka University, Suita 565, Japan.

Publisher Item Identifier S 0733-8716(97)03369-6.

the trailer behind the packet and directly divides the packetinto each 48-byte payload of the ATM layer. Furthermore,the ATM-layer-user-to-ATM-layer-user (AUU) parameter isprovided in the payload-type indication (PTI) field of the ATMcell header, and it indicates whether or not the cell is at theend of a packet; if the AUU of a cell is set to one, then the cellis so. As a result, in case of AAL5, the switch can recognizethe last cell of a packet only by observing the header of cells,without checking its payload.

There are mainly two types of selective cell discardschemes: tail dropping (TD), or partial packet discard (PPD) in[2]) and early packet discard (EPD). TD requires the switch todiscard all subsequent cells from a packet if one cell has beendropped. On the other hand, in applying EPD, the switch dropsentire packets when its queue length reaches a threshold level.We will call this EPD1. Romanow and Floyd [2] compare theperformance of TD with that of EPD1 in regard to throughput,and suggest that EPD1 achieves higher throughput than TD.Furthermore, in [3], by extending the EPD method, in whichthe switch sets up variable thresholds depending on the numberof accepted packets, better performance than EPD1 is thusobtained. It will be referred to as EPD2 in this paper.

The above studies were carried out by simulation, and it wassupposed that the packet length is fixed. In order to analyticallyevaluate the performance, once a cell is lost, we must keeptrack of the cells following the lost cell until the last cell ofthe packet arrives. Such kinds of analyses have already beenproposed (e.g., see [5] and [6]). However, it becomes hard totreat the case where the packet size is relatively large sincethe number of states kept in the analysis grows explosively.Kamal [4] deals with a tractable model for the tagged source toonly analyze TD by supposing that the packet length follows ageometric distribution in terms of cells, i.e., we do not requirememorizing the states of the packet length. However, thisanalysis is an approximate one in terms of modeling othersources. In this paper, we propose the exact analysis of TDby the following assumptions: the distribution of the packetlength from AAL5 traffic is a geometric one, and sources arehomogeneous in terms of traffic characteristics. Furthermore,we extend the analysis to treat the cases of both EPD1 andEPD2. Thus, we extensively investigate the impact of thebuffer size, the number of sources, and traffic characteristicson the effectiveness of selective cell discard schemes.

The remainder of this paper is organized as follows. InSection II, we describe our analytical model and explain theselective cell discard scheme in detail. In Section III, we

0733–8716/97$10.00 1997 IEEE

904 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 15, NO. 5, JUNE 1997

Fig. 1. Multiplexer model to discard corrupted packets.

define the states of each source, and derive the steady-stateprobability and the packet loss probability in TD, EPD1,and EPD2, respectively. Section IV provides the numericalresults to investigate the influence of traffic characteristicson the packet loss probability. Finally, Section IV providesconcluding remarks.

II. M ODEL AND SELECTIVE CELL DISCARD SCHEMES

A. Model Description

We consider a discrete-time queueing system with time slotbeing equal to a cell transmission time. In our model, thereare sources transmitting their cells to a multiplexing nodeor a switch with an output buffer of cells as illustrated inFig. 1. We suppose that sources are homogeneous in terms oftraffic characteristics. Each source generates cells according toan interrupted Bernoulli process (IBP), which is characterizedby a parameter set of . IBP has two states: an onstate and an off state. In each slot, the process changes itsstate from on to off with probability , and from off to onwith probability . In the on state, one cell arrives in eachslot with probability , while no cell arrives in the off state.Thus, the average arrival rate of each source is given by

(1)

As shown in [7], the burst length of IBP, which indicates thenumber of cells generating in an on period, follows a geometricdistribution with parameter , where

(2)

It follows that the average burst length is equal to .Furthermore, we assume that a burst consists of exactly onepacket; the distribution of the packet length is a geometric onewith parameter and the average packet length isgiven by .

B. Selective Cell Discard Schemes

1) Tail Dropping, TD: As previously mentioned, once oneof the cells constituting a packet is lost, the subsequent cells ofthe corrupted packet result in wasting network resources. Thus,under TD, the switch discards such cells instead of relayingthem even if the buffer can accommodate them [1]–[4]. Thisprevents those cells from wasting network resources, and willcontribute to reducing the number of corrupted packets.

Fig. 2. Definition of states in source. 1) Cell is lost due to buffer overflow.2) Subsequent cells are dropped by force.

2) Early Packet Discard, EPD:EPD enforces a switch todrop entire packets prior to its buffer overflow. If the first cellof a packet arrives at a switch when the number of cells in thebuffer is more than or equal to some threshold, the first cell isdiscarded, as well as its subsequent cells. Consequently, thatpacket will be dropped entirely. In addition, once a cell of anaccepted packet is lost due to buffer overflow, its subsequentcells are also dropped as in TD. Two kinds of EPD’s areconsidered. One EPD is based upon a fixed threshold (EPD1)[2], and the other (EPD2) is based upon a variable thresholdwhich is a function of the number of ongoing packets whichwere already accepted [3].

III. A NALYSIS

In this section, we will derive the steady state probabilityand the packet loss probability in the system where TD, EPD1,or EPD2 is applied in the switch.

First, for this purpose, we define the states of each sourceas shown in Fig. 2:

• off: the source does not generate a packet;• on: the source is transmitting a packet and no cells have

been lost;• on : the source is transmitting a packet, and one or more

cells of the packet have already been discarded.

Since sources are homogeneous, we can completely describethe state of our system at theth slot by a set of: 1) the queuelength of the switch, 2) the number of sources inthe on state, and 3) the number of sources in the onstate. The system stateforms a discrete-time Markov chain with finite states. Notethat when and , the number ofsources in the off state at theth slot is given by ,where denotes the number of sources in our system. Here,we define as the state space for , i.e.,

. A state is labeledusing the following one-to-one mapping function [8]

(3)

Therefore, can be equivalently represented by the state space, where .

A. Analysis of TD

We assume that phase state transitions of IBP occur justafter cell generations from each source. We first define the cellarrival probability at the switch and the transition probabilityof the number of sources in each state.

KAWAHARA et al.: PACKET LOSS OF CELL DISCARD SCHEMES 905

Fig. 3. Transition diagram of the number of sources in each state, focusedon that in the on state for TD.

1) Cell Arrival Probability at the Switch:We defineas the probability that cells arrive at the switch

from sources being in the on state when and. Note that cells generated at the source being

in the on state are dropped, and cannot enter the buffer ofthe switch. Thus, is independent of , andis given as follows:

(4)

The matrix representation takes the following form:

diag (5)

2) Transition Probability of the Number of Sources Being inEach State:We obtain below the transition probability of thenumber of sources being in each state under the conditionthat cells are lost in a slot. Let denote a randomvariable which represents the number of cells lost due to bufferoverflow at the th slot. Fig. 3 illustrates the transition diagramin the case of . Defining the following probability:

(6)

we derive it by means of the transition diagram shown inFig. 3 as follows.

Suppose that cells from sources are lost due to bufferoverflow; then sources among thosesources change theirstates to the on state and, on the other hand,- sourceschange their states to the off-state because lost cells are thelast ones of the packets. Furthermore,sources being inthe on state are assumed to keep their states. Table I showsthe transition of the number of sources in this case. Therightmost column (the bottom row) represents the number of

TABLE ITRANSITION OF THE NUMBER OF SOURCES IN EACH STATE FOR TD

sources in each state before (after) the transition. We thushave as

if

if(7)

Furthermore, we define as

......

... (8)

3) Steady-State Probability of Our System:We define thesystem state probability at theth slot as

(9)and introduce its vector representation

Letting denote the transition matrix whose elementsrepresent the probabilities thatcells arrive given that cellsout of those cells are lost at the switch, we have

(10)

Further, we define the following:

(11)

As a result, is related to as follows:

if

ifif

(12)


The transition probability matrix of the TD system thusbecomes

......

......

......

......

......

...

(13)

where represents a zero matrix of dimension .Furthermore, the steady-state probability of the system is givenby

(14)

and its vector is represented by

Consequently, we can obtain by solving the followingequation:

(15)

where represents a column vector of dimension,whose elements are all equal to one.

It may be difficult to directly solve (15) since the number ofstates grows explosively as the buffer sizebecomes large.The algorithm proposed in [9] enables us to calculateevenfor a large .

4) Derivation of Packet Loss Probability:Fig. 3 is veryhelpful in deriving the packet loss probability. First, the packetgeneration corresponds to a transition of the state from the offstate to the on state in Fig. 3. Next, when the packet is (not)successfully relayed, the state of the source finally returnsto the off state from the on state (onstate). Consequently,the packet loss probability is given by the ratio of the meannumber of sources which change their states from the onstate to the off state to the mean number of sources whichchange from the off state to the on state in a slot.

First, let denote the mean number of sources whichchange their states to the off state with packet loss in a slot.There exist two related transitions from the onstate to theoff state in Fig. 3. One of them, in fact, comes to the off statedirectly from the on state. This transition corresponds to thephenomenon that only the last cell of a packet is discardedand the state changes to the off state at the following slot. Themean number of sources which take this transition in a slot isdenoted by . We also denote the mean number of sources

which change their states from the onstate to the off state ina slot by . Thus, and are given as follows:

As a result, becomes

(16)

Next, let denote the mean number of packets generatingin a slot. Note that there is a possibility that a source generatesno packet during the on state. Let denote the probability ofno packet generation in an on period of IBP. Thus, lettingdenote the mean number of sources which change their statesfrom the off state, we have

(17)

where and are given by

Finally, by using and , we obtain the packet lossprobability

(18)

B. Analysis of EPD1

Next, we provide the analysis of EPD1. Under this scheme,the switch discards an entire packet if the first arriving cell ofthe packet arrives there when the number of cells in its bufferis more than or equal to a threshold.

The transition probability associated with the number ofsources being in each state, derived in Section III-A2, underTD, is the same as that given by (7), except in the caseof the transition diagram is presented inFig. 4. In that case, the transition probability [correspondingto ] is denoted by . Tran-sitions from the off state to the on state there do not occur, buttransitions from the off state to the onstate do, differentlyfrom those in the case of TD. Noting this feature, we obtain the


Fig. 4. Transition diagram of the number of sources for EPD.

transitions related to as shown in Table II.We hence have

ifif

(19)

and its matrix representation as follows:

......

... (20)

1) Derivation of Packet Loss Probability:When, the probability matrix corresponding to

becomes

(21)

The relation between and can be obtained in asimilar way to Section III-A3 as follows:

if

ifif

(22)

where and are given in (11), and

(23)

TABLE IITRANSITION OF THE NUMBER OF SOURCES IN CASE WHEREb � H FOR EPD1

Hence, the transition matrix for EPD1 is given by

......

......

......

......

......

......

......

......

...

(24)

and the steady-state probability vectoris obtained from (15).We derive the packet loss probability for EPD1 in the

same way as that for TD [namely, by using (18)] except forthe following: when , a source may generateno packet after its transition from the off state to the onstateuntil it returns to the off state. The mean number of sourceswhich take such a transition in a slot is denoted by. Wethen have

(25)

Note that, on average, sources generate no packets amongsources which change their states from the onstate to the offstate in a slot. Thus, in EPD1, in (18) should be rewritten as

(26)

while in (18) is the same as that in (17).

C. Analysis of EPD2

In EPD2, the threshold at theth slot depends on the numberof accepted packets, and is determined in a way to

prevent cells of already accepted packets from being lost dueto buffer overflow. Since a number of cells in an acceptedpacket have already left the switch, each accepted packet mayactually require the buffer capacity of less than the averagepacket length (cells).

For these reasons, Noritakeet al. in [3] have introduced aparameter , which will be called theacceptancecoefficient, and the threshold depending on

as follows:

(27)


Thus, a newly arriving packet is more likely to be discardedas more packets already have been accepted since

. Note also that should be determined in sucha way as to provide low packet loss probability; this will bediscussed later based on numerical results.

The transition probability matrix corresponding to (20)depends on the current value of the threshold. Let denotethe conditional transition probability matrix, given that newlyarriving packets are discarded ifpackets or more are alreadyaccepted. We then have

......

... (28)

where

[given in (7)] if[given in (19)] if (29)

Let denote the transition probability matrix whencells arrive and cells are lost due to buffer overflow under

the same condition as that of . is given by

(30)

and we define the following:

Note that and are constructedto represent the transition when the queue length ofthe switch satisfiesor . For example, all of the transitionprobabilities from states withto states with are represented by

. Note also that when the queue length is lessthan , all of the transitions are governed by or .We shall explain this fact below. First of all, when ,none of the newly arriving packets is discarded due to EPD.On the other hand, and represent transitions withEPD, which is effective only if . However, since thenumber of sources in the system is assumed to beimplies that no source changes its state from the off state tothe on state; no new packets are generated. Thus, and

are considered to represent transitions without EPD, andtherefore we can apply these matrices to the caseas well as .

Accordingly, by using or for such that satisfies, we can relate with

as follows:

if

ifif

(31)

The transition matrix for EPD2 becomes

......

......

......

......

......

......

......

......

...

(32)

and the steady-state probability vectoris obtained from (15).We derive in EPD2, which is given by (25) in the case

of EPD1 as

Thus, by using (17), (18), and (26), we finally obtain the packetloss probability for EPD2.


Fig. 5. Distribution of the queue length.

IV. NUMERICAL RESULTS AND DISCUSSIONS

In this section, we evaluate the performance of selective celldiscard schemes using the analysis presented in the precedingsection.

A. Effectiveness of TD

We compare the performance of TD with that of the systemwith no control, which is denoted NC for short, and investigatethe impact of the buffer size and the number of sources onthe performance. In order to estimate the improvement of thepacket loss probability by TD, we first represent thedistribution of the queue length and the average number ofsources in each state.

Fig. 5 shows the distribution of the queue lengthin thesteady state, which is given by

where indicates a dimension of the vector. The meanpacket size is fixed to 10 (cells) in this figure. We alsoset the buffer size of the switch to 50 (cells), the arrivalrate in the on period (namely, peak rate) of IBP to 0.15,and the total arrival rate at the switch to 0.7. Inthis setting, we change the numberof sources to 5, 10, and15. We observe a little difference between the distributions ofTD and NC only when the queue length is greater than about45 for all .

Table III shows the average number of sources in each statein the same setting as in Fig. 5. Let anddenote the average number of sources in the on state, onstate, and off state, respectively. We then have

By applying TD, becomes larger and becomessmaller than those of NC, while does not change. The

TABLE IIIAVERAGE NUMBER OF SOURCES IN EACH STATE FOR SOME VALUES OFR

Fig. 6. Packet loss probability as a function of the buffer sizeB of the node.

probability that each source is in the off state is given byThe probability of the

number of sources being in the off state follows the binomialdistribution with parameters ; its averagethus becomes equal to . From (1) and the definitionof , we can simply rewrite as

(33)

Note also that the sum of and is kept constant evenwhen changes since it is equal to [see (33)], whichis independent of .

We expect from Fig. 5 and Table III that TD makes thepacket loss probability better than NC. Fig. 6 illustrates

as a function of the buffer size of the switch. Whendrastically decreases asincreases. We compare

the ratio of in NC to that in TD when . Forand , the ratio is equal to

and , respectively, namely, TD is more effective for alarger . On the other hand, Fig. 6 shows that the ratio iskept almost the same for each while varies. Thus, weconclude that the effectiveness of TD is almost insensitive tothe buffer size.

B. Impact of Traffic Parameters on PacketLoss Probability of TD

In this subsection, we investigate the impact of the peak rate, the total arrival rate and the mean packet length

on the packet loss probability . Fig. 7 shows as afunction of . In this figure, we fix and

while takes 0.1, 0.15, 0.3, and 0.5. Note here thatwe should vary by changing the probability of IBP whilethe probability remains fixed since the average packet length

is a function of as shown in (2). Therefore, from (1),increases with . It is seen from the figure that the difference


Fig. 7. Packet loss probability as a function of the total arrival rate�all

atthe node.

Fig. 8. Impact of the packet lengthLp.

between in TD and that in NC gets larger as either orbecomes larger, although it is not significant. We also say

that TD is more effective as the average off period becomessmaller because the average off period can be defined by.

Fig. 8 shows the impact of on . The differencebetween in TD and that in NC gets larger as becomeslarger. In addition, Table IV gives the average number ofsources in each state. Note that the sum of and isconstant for any value of because it is given by .We see that TD is more effective in decreasing in thecase of than in the case of . We shallshow below what leads to this feature. As the average packetlength becomes larger, it is very likely that there would bemore cells following the first lost cell. Thus, since TD canget rid of such cells that will waste the buffer capacity, TDwill be more effective in using the buffer capacity efficientlyfor a longer packet. In fact, as shown in Fig. 9, illustratingthe distribution of the queue length in cases of and

TD successfully prevents the buffer from being filled withcells; TD reduces the probability of the buffer being full ofcells from about 0.01 to 0.001 when .

C. Effectiveness of EPD Schemes When

Fig. 10 shows the packet loss probability as a functionof the threshold of EPD1. of both NC and TD arealso given for comparison. The related parameters are set

TABLE IVAVERAGE NUMBER OF SOURCES IN EACH STATE: CASES OFLp = 10 AND 100

Fig. 9. Distribution of the queue length: cases ofLp = 10 and100.

Fig. 10. Packet loss probability as a function of the thresholdH of EPD1.

as follows: and. The figure shows that of EPD1 gets smaller

as becomes larger, but it eventually cannot become smallerthan that of TD. On the other hand, Fig. 11 illustrates thedistribution of the queue length in the cases of and40. The buffer is less congested in the case of thanin the case of , whereas is larger in the formercase than in the latter case. EPD1 with a smaller thresholdsuccessfully makes the buffer less congested at the cost ofdiscarding newly arriving packets earlier. Namely, a smallerthreshold can decrease the loss probability of already acceptedpackets, while it can increase that of newly arriving packets.Hence, we expected that there would exist some thresholdthat provided a smaller than that in TD. However, thesefigures show that EPD1 does not succeed in improving .

Fig. 12 shows as a function of for EPD2. The relatedparameters are set as in Fig. 10 for EPD1. It is shown in this


Fig. 11. Distribution of the queue length: cases ofHb = 20 and40.

Fig. 12. Packet loss probability as a function of� for EPD2.

figure that a larger causes more packets to be lost; whenexceeds , EPD2 cannot improve at all compared withNC. We shall compare of EPD2 with that of EPD1, forexample, in the case of . When and

, a set of thresholds becomesfrom (27), i.e., no newly arriving packets

are discarded until the queue length of the switch reaches.In Fig. 10, when of EPD1 is about 5 10whereas of EPD2 is about 3 10 if . Thissuggests that the threshold should be determined dependingon the number of accepted packets, unlike in EPD1. However,like EPD1, EPD2 does not perform better than TD.

In order to show the reason why EPD’s do not outperformTD in the numerical results presented above, we illustrate inFig. 13 the distribution of the number of lost packets obtainedby simulation in the cases of TD/EPD1 with the threshold

and EPD2 with the acceptance coefficient .In the simulation, the run time is set to 10slots, and allassumptions and parameters are set to the same as those inthe analysis. We can observe that TD drastically reduces thenumber of lost packets of one to around 20 cells in length incomparison with EPD’s. On the other hand, the number of lostpackets of length greater than 20 cells is less in EPD’s than inTD, not a remarkable difference. From this figure, we see thatEPD’s prevent longer packets from being discarded very well,whereas TD prevents shorter packets. In addition, we see that

Fig. 13. Distribution of the number of lost packets (obtained by simulation).

Fig. 14. Packet loss probability as a function of the thresholdH:Lp = 50; 200; and 1000.

EPD2 outperforms EPD1 when the packet length is smallerthan around 20. In the following section, we will investigatethe impact of the average packet length.

D. Effectiveness of EPD Schemes in Caseof the Relatively Large

First, Fig. 14 illustrates the packet loss probability as afunction of the threshold of EPD1 in cases of the averagepacket length and . We observe that when

of EPD1 gets larger as becomes smaller,whereas of EPD1 is smaller than that of TD, and isminimized at and when is and ,respectively. Next, Fig. 15 represents as a function of

for EPD2 in cases of and . We canalso find from this figure that EPD2 performs better than TDwhen and while EPD2 does not improve

when .Finally, we compare the packet loss probability of TD,

EPD1, and EPD2 as shown in Table V. Let and denotethe threshold and the product of the acceptance coefficient andthe average packet length minimizing under EPD1 and


Fig. 15. Packet loss probability as a function of�Lp: Lp = 50; 200; and1000.

TABLE VCOMPARISON OFPACKET LOSS PROBABILITY OF TD, EPD1,AND EPD2

EPD2, respectively. We observe from this table that EPD1performs better than TD when gets larger than 200, EPD2performs better when it is larger than , and that EPD2always outperforms EPD1. As gets larger, of EPD1gets smaller and becomes larger. Recall that, in ourassumption, both the EPD1 and EPD2 schemes also apply TDwhen cells of accepted packets get lost due to buffer overflow.Therefore, both EPD1 and EPD2 are quite similar schemes asTD when of EPD1 and of EPD2.

V. CONCLUSION

Selective cell discard schemes, such as tail dropping (TD)and early packet discard (EPD), have been considered as away to efficiently utilize the network resources by selectivelydiscarding cells or packets that are not worth relaying withinthe network. In this paper, we carried out an exact analysisof the packet loss probability in the cases of TD, EPD basedupon a fixed threshold (EPD1), and that based upon variablethresholds (EPD2), given that the packet length follows ageometric distribution, and that sources are homogeneous interms of traffic characteristics. So far, the related works havebeen based upon simulations or an approximate analysis.

We have obtained the following results by means of numeri-cal ones. In comparison with the packet loss probability underno control, TD reduces the packet loss probability slightly,and TD is more effective in doing so as the total arrival rateat the switch, the peak rate of each source, and the numberof sources becomes larger, while the performance of TD isinsensitive to the buffer size of the switch.

On the other hand, the performance of EPD’s stronglydepends on the average packet length. The optimal value,which minimizes the packet loss probability, of the threshold

of EPD1 gets smaller, and that of the product of theacceptance coefficient and for EPD2 becomes larger as

gets larger. Furthermore, EPD’s perform better than TDwhen is greater than about 100. Thus, we conclude thatfor a much shorter length of the packet, only TD may beemployed as the selective cell discard scheme to improve thepacket loss probability. Furthermore, it is easier to implementthe mechanism of TD on ATM switches than EPD’s. However,as shown in [2], EPD’s provide better throughput performancethan TD when packets are of fixed size, and Turner [10]suggests that some kinds of EPD schemes achieve fairnessof each connection. Therefore, clarifying these topics will beleft for further study.

REFERENCES

[1] G. J. Armitage and K. M. Adams, “Packet reassembly during cell loss,”IEEE Network, vol. 7, pp. 26–34, Sept. 1993.

[2] A. Romanow and S. Floyd, “Dynamics of TCP traffic over ATMnetworks,” IEEE J. Select. Areas Commun., vol. 13, pp. 633–641, May1995.

[3] K. Noritake, S. Ushijima, and M. Hirano, “A study on selective celldiscard control in ATM-CL network,” IEICE Tech. Rep., SSE94-77,June 1994.

[4] A. E. Kamal, “A performance study on the effect of the end-of-messageindicator in AAL type 5,” inProc. IEEE INFOCOM’95, pp. 1264–1272.

[5] I. Cidon, A. Khamisy, and M. Sidi, “Analysis of packet loss processes inhigh-speed networks,”IEEE Trans. Inform. Theory, vol. 39, pp. 98–108,Jan. 1993.

[6] K. Kawahara, K. Kumazoe, T. Takine, and Y. Oie, “Forward errorcorrection in ATM networks: An analysis of cell loss distribution ina block,” in Proc. IEEE INFOCOM’94, pp. 1150–1159.

[7] K. Kumazoe, K. Kawahara, T. Takine, and Y. Oie, “Analysis ofpacket loss in transport layer over ATM networks,” inProc. IEEEGLOBECOM’96, pp. 42–49.

[8] C. G. Kang and H. H. Tan, “Queueing analysis of explicit priorityassignment partial buffer sharing schemes for ATM networks,” inProc.IEEE INFOCOM’93, pp. 810–819.

[9] T. Takine, T. Suda, and T. Hasegawa, “Cell loss and output processanalyzes of a finite-buffer discrete-time ATM queueing system withcorrelated arrivals,”IEEE Trans. Commun., vol. 43, pp. 1022–1037,Feb.-Mar.-Apr. 1995.

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Kenji Kawahara received the B.E. and M.E. de-grees in computer sciences and electronics fromKyushu Institute of Technology, Iizuka, Japan, in1991 and 1993, respectively, and the Ph.D. degreein information and computer science from OsakaUniversity, Osaka, Japan, in 1996.

From 1995 to 1997, he was an Assistant Professorin the Information Technology Center, Nara Instituteof Science and Technology. Since April 1997, hehas been an Assistant Professor in the Departmentof Computer Science and Electronics, Faculty of

Computer Science and Systems Engineering, Kyushu Institute of Technology.His research interests include computer networks, error, and congestion controlin high-speed networks.

Dr. Kawahara is a member of the IEICE.


Koichiro Kitajima was born in Kumamoto, Japan,in 1971. He received the B.E. and M.E. degreesin computer sciences and electronics from KyushuInstitute of Technology, Iizuka, Japan, in 1994 and1996, respectively.

Since 1996, he has worked at Fuji Xerox Com-pany, Ltd., Tokyo.

Mr. Kitajima is a member of the IEICE.

Tetsuya Takine (M’94) received B.Eng., M.Eng.,and Dr. Eng. degrees in applied mathematics andphysics from Kyoto University, Kyoto, Japan, in1984, 1986, and 1989, respectively.

In April 1989, he joined the Department of Ap-plied Mathematics and Physics, Faculty of Engi-neering, Kyoto University, as an Assistant Profes-sor. Beginning in November 1991, he spent oneyear at the Department of Information and ComputerScience, University of California, Irvine, on leave ofabsence from Kyoto University. In April 1994, he

joined the Department of Information Systems Engineering, Faculty of Engi-neering, Osaka University, as a Lecturer, and since December 1994, he hasbeen an Associate Professor in the same department. His research interests in-clude queueing theory and performance analysis of computer/communicationsystems.

Dr. Takine is a member of the ISCIE, ORSJ, IPSJ, and IEICE.

Yuji Oie (M’83) received the B.E., M.E. and D.E.degrees from Kyoto University, Kyoto, Japan, in1978, 1980, and 1987, respectively.

From 1980 to 1983, he worked at Nippon DensoCompany Ltd., Kariya, Japan. From 1983 to 1990,he was with the Department of Electrical Engi-neering, Sasebo College of Technology, Sasebo,Japan. From 1990 to 1995, he was an AssociateProfessor in the Department of Computer Scienceand Electronics, Faculty of Computer Science andSystems Engineering, Kyushu Institute of Technol-

ogy, Iizuka, Japan. From 1995 to 1997, he was a Professor in the InformationTechnology Center, Nara Institute of Science and Technology. Since April1997, he has been a Professor in the Department of Computer Science andElectronics, Faculty of Computer Science and Systems Engineering, KyushuInstitute of Technology. His research interests include performance evaluationof computer communication networks, high-speed networks, and queueingsystems.

Dr. Oie is a member of the IPSJ and IEICE.

packet loss performance of selective cell discard schemes in atm switches

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