THROUGHPUT EVALUATION OF AN ASYMMETRICAL FDDI TOKEN RING NETWORK WITH MULTIPLE CLASSES OF TRAFFIC

Transcription

1 THROUGHPUT EVALUATION OF AN ASYMMETRICAL FDDI TOKEN RING NETWORK WITH MULTIPLE CLASSES OF TRAFFIC Priya N. Werahera and Anura P. Jayasumana Department of Eletrial Engineering Colorado State University Fort Collins, Colorado Abstrat The Fiber Distributed Data Interfae (FDDI) standard supports synhronous and asynhronous data transmissions. It allows eah station to have multiple lasses of asynhronous data, and meets the requirements of different lasses by means of a timer-based priority sheme. The performane of a nonhomogeneous FDDI network arrying multiple lasses of traffi is onsidered. An analytial model is presented to evaluate the throughput of synhronous traffi and asynhronous traffi. This model an be used to evaluate the throughput of individual priority lasses and the mean token-yle time of the network. A method to selet timers to support integrated synhronous and asynhronous traffi in FDDI is presented. Simulations are used to verify the analytial model. Simulation results are also used to examine the variation of the mean message-delay harateristis of various lasses. Limitations of the model are outlined. I. Introdution The FDDI provides high bandwidth general purpose interonnetions using fiber optis as the physial medium in a token-ring onfiguration [1,2]. It supports two major lasses of traffi: synhronous lass and asynhronous lass. Synhronous lass provides a prealloated bandwidth and a guaranteed response time, and may be used for time ritial messages suh as voie and video signais. The remaining bandwidth is dynamially alloated to asynhronous lasses with non-time ritial messages suh as data [l]. The FDDI standard supports multiple lasses of asynhronous traffi by means of a timer-based priority mehanism. The priority mehanism is very similar to that of the IEEE token-passing sheme. In FDDI priority sheme, the transmission time of all the messages of a node in the previous yle is inluded in the urrent token-yle time measured by that node. In IEEE token-passing bus priority sheme, the urrent token-rotation timer is initialized only after the queue of that lass reeives the token. Thus the token-yle time for a lass does not inlude the interval the node used for transmitting higher priority messages in the previous rotation.... This work was supported in part by the CSU Superomputer Projet. Analytial and simulation models have been used to evaluate the performane of the priority sheme for homogeneous token-passing bus networks supporting multiple lasses of traffi [3-71. In a homogeneous network, all stations are idential. Performane of networks for time ritial messages has been investigated in [ A non-homogeneous token-passing bus network is analyzed in [ll] under heavy traffi. Based on the priority sheme, the network is transformed into a set of queues where eah queue represents a priority lass at a node in the original network. It also neglets the overflow transmission of messages. Due to the differene between the priority shemes, this form of transformation annot be done for FDDI networks. The model presented in this paper predits the throughput of FDDI priority sheme at both normal and heavy load onditions. A timer-based token-ring network is analyzed in [12] using simple approximations to evaluate the performane of a network similar to FDDI. An expression is given for the overall maximum ring utilization, but no results are provided on the throughput of individual priority lasses. An analytial model is proposed in [13] to predit the throughput of a nonhomogeneous FDDI network. This model however, allows only one priority lass per station and does not onsider the synhronous traffi. It is important to onsider the synhronous traffi to fully understand the behavior of FDDI sine synhronous traffi an affet the throughput a.nd the message-delay of asynhronous traffi. The model we present in this paper allows multiple lasses of priorities at a given station. It does not however, expliitly over the ase onsidered in [13]. Simulation results are presented in [14] for an FDDI network supporting paketized voie. A homogeneous network is onsidered with only a single asynhronous priority lass. A performane omparison of FDDI network and the token-ring network with a reservation sheme is given in [15]. Comparisons are based on the fairness of the priority sheme, ability to distinguish between time ritial messages (ex. alarm signal) and messages that need guaranteed response time and bandwidth (ex. voie, video signals) et. The relationship between the asynhronous throughput and the network parameters is onsidered in [16]. In this paper, we evaluate the performane of a nonhomogeneous FDDI token-ring network, in the presene of synhronous traffi and asynhronous traffi. Voie signals are used to represent synhronous traffi, but any other synhronous traffi type may be used instead. We have onsidered CH2826-5/90/0000/0997/$01.OO IEEE 991

2 three types of stations onneted to the ring: stations that support synhronous traffi or voie only stations, stations that support asynhronous traffi or data only stations, and stations that support both synhronous traffi and asynhronous traffi or voie and data stations. The analytial results in Setion I11 are derived on the assumption that there is at least one of eah voie and data and data only stations onneted to the ring. The synhronous traffi and the asynhronous traffi load of the network is equally distributed among the stations that support the respetive traffi lasses. The asynhronous traffi load at a station is distributed among three lasses of priorities. The asynhronous traffi may be asymmetrially distributed among these three lasses of priorities. A brief desription of the FDDI protool is given in Setion II. Performane of FDDI protool is evaluated in Setion 111. Analytial expressions are developed to evaluate the throughput harateristis of the different lasses of messages. FDDI protool parameters are alulated to meet speifi traffi requirements in Setion IV. The analytial results are verified using simulations in Setion V. Mean message-delay for different lasses obtained from the omputer simulations are presented. The limitations of this work are outlined in Setion VI. 11. FDDI Protool Desription In an FDDI token-ring network [1,2], any station may apture the token by removing it from the ring. After the removal of the token, the station may begin to transmit information frame(s). When the information transmission is ompleted, the station immediately issues a new token. FDDI standard supports two types of traffi: (1)Synhronous traffi: A lass of data transmission servie whereby eah requester is prealloated a maximum bandwidth and guaranteed a response time not to exeed a speifi delay. (2)Asynhronous traffi: A lass of data transmission servie where by all requests for servie ontend for a pool of dynamially alloated ring bandwidth and response time. A set of timers and several parameters are used to limit the length of time a station may transmit messages before passing the token to the next station and the duration of information transmission of eah lass within a station. Eah station maintains two timers, the Token-Rotation-Timer (TRT) and the Token-Holding-Timer (THT). TRT at node j is used to time the interval taken by the token to irulate around the ring starting from node j. When node j reaptures the token, TRT is reset and restarted immediately. Before resetting TRT, its urrent value is assigned to THT. TRT and THT both beome ative during message transmission at node j. THT is reset when the token is passed to the next station, and it beomes inative while TRT ontinues to run until the token arrives at node j again. During ring initialization, all the stations negotiate a value for the parameter alled the Target-Token- Rotation-Time (TTRT). At the end of the negotiation period, the smallest TTRT requested beomes the operative TTRT for the network and the T-Opr in eah station is set to this value. If a station aptures the token before its TRT reahes the value of TTRT, it is an early token. If it aptures the token after TRT has exeeded the value of TTRT, then it is a late token. An early token may be used to transmit both synhronous and asynhronous traffi while a late token may only be used for synhron bus traffi. We use the term High-Priority- Token-Time (T,) to denote the duration for whih a station is allowed to initiate the transmission of the synhronous messages. If the token is late, the station will issue a new token immediately after transmitting synhronous traffi for a duration of T,. For an early token, the station is allowed to transmit asynhronous traffi provided the urrent value of THT is less than the value of TTRT. The differene between the urrent value of THT and TTRT determines the asynhronous bandwidth available to this station. FDDI standard also supports a priority sheme for asynhronous traffi. Eah priority lass at a station has a threshold value T-Pri(i) (i=l,..,n). Class 1 is assumed to have the highest priority, and lass n the lowest priority among asynhronous lasses of traffi. Transmission of messages of an asynhronous lass begins with lass 1 and ontinues with the lower priority lasses sequentially. The asynhronous traffi of lass i may only be transmitted if the urrent value of THT is less than the lass threshold value T-Pn(i). Sine, the differene between the urrent value of THT and TTRT reflets the asynhronous bandwidth, the maximum value that an be assigned to T-Pn(i) of lass I is restrited to TTRT. If there are no messages in lass I, or if the THT has exeeded the T-Pri(i), then the next lower lass is served. A new token is issued when there are no more messages, or the lowest priority lass has been served aording to the above sheme Performane Evaluation of FDDI The analysis assumes the error free operation of the network, i.e., all messages transmitted are reeived without any errors, no messages are lost, no failures in the transmission medium, stations, onnetors, et. Further, it is assumed that there is at least one voie and data station and one data only station onneted to the ring. A station has to wait until it ompletely removes the token from the ring before transmitting messages. This duration alled the token-apture time is very small and is negleted in the analytial model, but it is taken into aount in the simulation model. For asynhronous traffi, assume that the message length is exponentially distributed and that the message arrivals follow a Poisson proess. Speeh onversations are used to model synhronous traffi. These speeh onversations must be transformed into an aeptable form before transmission. The terminology used for network parameters and variables is summarized in Table I. N TTRT TR T TET T-Pri(i) TS CO T,,(i) TA total number of stations number of stations transmitting asynhronous traffi number of stations transmitting synhronous traffi target-token-rotation-time (bit times) token-rotation-timer (bit times) token-holding-timer (bit times) priority threshold value for asynhronous lass i (bit times) high-priority-token-time (bit times) token-yle time (bit times) no load token-yle time (bit times) mean-token-yle time (bit times) mean message length of lass i traffi (bits) number of overhead bits added to any paket (bits) Table I: Network parameters 998

3 All times are expressed in bit times, the time to transmit a single bit. We define a term, token-yle time as the time elapsed from the instant an aess lass at a station reeives the token till the next instant the same aess lass at the same station reeives the token. This definition of token-yle time is used in the following analysis and it is different from TRT of FDDI network. CO is the no load token-yle time. C is the mean token-yle time averaged over all the stations. Throughput of a network S is defined as the total number of data bits reeived at the destination per seond, expressed as a fration of the bandwidth. Utilization U of a network refers to the fration of time the network spends arrying the data pakets inluding header information. In an error free network, (1 - U) is the fration of time spent on token transmission. The offered load G is defined as the total number of data bits generated by all ative stations per unit time (expressed as a fration of the bandwidth). For individual lasses, the omponents S,, U, and C, an be defined in a similar manner. In this analysis, we onsider four lasses; lass 0 orresponds to synhronous traffi and lasses 1, 2 and 3 orrespond to asynhronous traffi. As a data frame inludes header information, heksum et, in addition to the data field, the throughput is always less than the utilization. The relation between throughput and utilization is given by, S, = (I,.U,, :=0,1,2,3 (1) where, (I, = T,(i) / [T,(:) + T,,]. The relative magnitudes of the lass thresholds affet the performane of a timer-based priority sheme [3-81. Assume that the lass thresholds are suh that, TTRT > T-Prr(1) > 2 -Pn(2) > T-Pn(3). (2) This ondition ensures that lass 1 messages reeive a higher bandwidth alloation than lasses 2 and 3. The mode1 an however be extended to over other ases. The network utilization U is given by [3], (e- CO) U = (3) In this paper, we selet the network parameters suh that all the synhronous traffi generated at stations are transmitted with bounded delay at any load ondition. Hene, So = Go. In our analysis, we assume a onstant synhronous load, i.e., that Go, So and U, remain onstant. Now onsider a network with synhronous traffi and asynhronous traffi. The asynhronous traffi present at a station is assumed to be divided among lass 1, lass 2 and lass 3 to a ratio of I, : 1, : I,. Under very low load onditions, all of the messages generated in all the lasses will be transmitted. Hene S, = G, for i = 0,1,2,3. Consider the ase where asynhronous traffi intensity is gradually inreased. The network will transmit messages of all four lasses until the network load exeeds a ertain value. However, the network will not be able to transmit all the traffi after the network load exeeds this value. Sine, TPri(1) > T-Pn(2) > T_Pri(3), the network will now transmit all of lass 0 lass 1 and lass 2 messages, but will not transmit some of lass 3 massages. The throughput of lass 3 reahes a peak when all of lass 3 messages in the network get barely transmitted over the transmission medium. Further inrease of load will result in a derease of throughput to aommodate traffi of lasses 1 and 2. In this analysis, we have onsidered three types of sta- t TRT- E -Time t THT= T-Pri(3) + T;,(3) Figure 1. The limiting ase for whih all lass 3 messages at voie and data stations get transmitted. tions. Out of these three types, the lass 3 traffi at the voie and data stations reah this limit first. This is due to the fat that voie and data stations have to transmit lass 0 traffi in addition to lass 1 and 2 traffi ahead of lass 3 traffi. This is illustrated in Figure 1. A node is allowed to omplete the transmission even if the respetive timer expires one it begins transmitting a message. Sine the message length of asynhronous traffi is exponentially distributed, due to its memoryless property, the remaining portion of the message left for transmission after lok expires is also exponentially distributed with the same mean message length. When all lass 3 messages generated at voie and data stations barely get transmitted, C is suh that, where X,,(i) is the mean number of data bits transmitted by the asynhronous lass i of a station during a yle and Ya(i) is the number of overhead bits required to transmit X,(i) data bits for i = 1,2,3. Here it is assumed that there is at least one station generating both voie and data traffi. Sine, the offered load in lasses 1, 2 and 3 are distributed to a ratio of l1 : I, : I,, X,(1) :,Yo(%) : X,(3) = I, : I, : 1,. Assume that X,(i) >> Y,,(i) for i = 1,2,3, i.e., the number of overhead bits is muh smaller than the number of data bits. Therefore, (x,,(1) + y,,(l)) : (X,(2) y,(2)) : (Xa(3) + y,(3)) 11 : 12 : (3 3 and 11 X,(1) + YJl) = - ( XJ3) + YJ3) ) > 13 The utilization of an asynhronous lass i is thus given by, (5) ((XJi) + Y,(i)) Nd) U, = for :=1,2,3. (8) 999

4 Hene, the utilization of lass 3 is ((Xa(3) + Ya(3)) Nd) U, = (9) Eliminating ( X4(3) + Y,(3) ) from Equations (7) and (9), C an be expressed as E. = (10) (1 + Pa3 U31 where, E, = [ T-Pri(3) + T,,,(3) - T, ] and p43 = 1'1 '2 + '3l /[I3 NdI. Solving Equations (5), (6) and (a), the utilization of lasses 1 and 2 an be expressed in terms of U, as '1 U, = - U U, = - U3 ' 13 The total network utilization U is (11) (12) U = U, + U, + U, + U,, (13) where U is given by Equation (3). From Equations (3), (11) and (12), - CO 1, + I, + la -- - U, + U,. (14) 13 Using Equation (10) for C, we an solve Equation (14) for U, as (E. (1-Vo) - CO) U, = (15) (Ea Nd pa3 U, and U, an be evaluated using Equations (11) and (12) respetively as (E. (1-Uo) - CO) U, =, (16) (Ea Nd -i. Pa1 (E, (1-Uo) - CO) U, = (17) (Ea Nd + Pa2 ' where, pill = [I, + I, + Id / [ I, Nd] and Po2 = ['I + '2 + / ['Z Ndl' Sine all messages generated get transmitted, the offered load in this ase is equal to the lass throughput. Hene, G, = S, for i = 1,2,3. Therefore, from Equations (1) and (15)-(17) the maximum total network load G,, for whih all the arriving messages get transmitted an be written as, G, = 1-. (E, (1-Uo) - CO) =1 %! ao U0.(18) (Eo Nd Pol Po2 Po3 a3 I Hene, S, = G, for i=1,2,3 in the range 0 5 G, 5 G,, where G, is given by Equation (18). When the asynhronous traffi is further inreased, the throughput of lass 3 ontinues to deline in order to aommodate the inreasing loads of lasses 1 and 2. When the network load exeeds a ertain value, the lass 3 throughput beomes negligible. When 'data only' stations annot transmit any of lass 3 traffi, no lass 3 traffi in the network gets ever transmitted. The ondition, T-Pri(3) is at least several messages lengths less than T-pri(2) and T-Pri(l) ensures that the 4 inr-e ---irime 4 1 I I r. T_l'r1(3) Figure 2. The limiting ase for whih lass 3 throughput beomes negligible at 'data only' stations. throughput of lass 3 is zero. As shown in Figure 2, this situation arises when THT is at least equal to T-Pn(3) after transmitting lass 1 and lass 2 traffi. For this ase, C is given by, T-Pri(3) = + ( xb(1) + Yb(1) ) + ( + yb(2) ' (19) where X,(i) is the mean number of data bits transmitted by the asynhronous lass i during a yle and Y,(:) is the number of overhead bits. Here it is assumed that there is at least one station generating only data tr&. Sine, ( X,,(l) + Ya(t) ) :( X,(2) + Y,,(2) ) 1, : I,, the utilization of lass 1 and lass 2 for this ase is given by, Solving Equations (19), (20) and (21), we get following expressions for C: - 4 = (22) ( + Pb2 where, E, = T-Pri(S), pa, = [ I, + IJ / [ I, Nd]. The total network utilization U an be written as U = U, + U, + U,. (23) U, and U, an be evaluated using Equations (3), (20), (211, (22) and (23) respetively as follows: (l-uo) - U, = (24) Nd Pbl (E, (1-Uo) - CO) U, = (2.5) Nd + PbZ where, psl = [I, + IJ /[11 Nd]. The throughput of individual lasses an be found from Equation (1). Sine, all of lass 1 and 2 messages generated get transmitted, the offered load of lass 1 and 2 is equal to respetive lass throughput. G, = S, for i = 1,2 and S3 = 0. Therefore, the total network load G, an be written as

5 where, p,, = [l, + IJ /[I, Nd]. The term ontaining pb3 in Equation (26) is the offered load of lass 3 evaluated using the offered load of lass 1, i.e., G, : G, = I, : I,. Hene, S, = G, for : = 1,2 in the range G,, 5 G, 5 G,. S, in this range is found using linear interpolation of values at Go and G,. A similar analysis gives the following results for the ase when the throughput of lass 2 reahes its maximum. E, C= (27) ( 1 + Pz U, ) and the utilization of lass 1 and lass 2 for this ase is given by, (E, (1-Uo) - CO) U, = (28) Nd + 0) p1 (E, (1-Uo) - CO) U, = (29) Nd + PZ where, E, = [ T-Pn(2) + T,,,(2) - T, 1, pcl = [I, + /[I, Ndl and pz = [I, + IJ /[I, N,]. Then by a similar argument, the throughputs are given by G, = S, for I = 1,2 and S, =O. Therefore, the total network load G, an be written as (E, (1-Uo) - I- CO) Q1 Q2 G, = Nd + p1 PZ p3 I ao U,.(30) where, p3 = [I, + IJ / [ I, Nd]. The term ontaining p3 in Equation (30) is the offered load of lass 3 evaluated using the offered load of lass 1. Hene, S, = G, for : = 1,2 and S, = 0 in the range G, 5 G, _< G. The ondition, T-Pn(2) is at least several message lengths less than T-Pn(1) ensures that the throughput of lass 2 is zero when the traffi in the network is further inreased. Then C and the utilization of lass 1 an shown to be Ed = (31) ( + pdl (Ed (l-uo) - 0) U, = (32) (Ed Nd + 0) Pdl where, Ed = T-Pn(2) and p,, = 1 / Nd. Then, G, = S, and S, = S, = 0. Therefore, the total network offered load G, an be written as (Ed ( - O) - 0) G, = (Ed Nd + 0) Pdl PdZ Pd3 l (10 U,.(33) where, p,, = I, / [I, Nd] and pd3 = I, / [I, Nd]. The terms ontaining pd2 and p,, in Equation (33) are the offered load of lass 2 and lass 3 respetively, evaluated using the offered load of lass 1. However, Equation (33) an be simplified further to obtain the following expression for G,; (Ed ( - O) - 0) G, = [ Q1 + Qo 00. (34) (Ed Nd 0) Hene, S, = G, and S, = 0 in the range G, 5 G, 5 G,. S, in this range is found using linear interpolation of values at G, and G,. A similar analysis an be arried out for the ase where the throughput of lass 1 reahes maximum as a result Of inreased load. C and the utilization of lass 1 for this ase is = (35) ( 1 +Pel U, 1 ( e (1-UO) - CO) U, = (36) Nd + 0) pel where, E. = [ T-Pri(1) + T,,,(1) + T, ] and pel = 1 / Nd. Then, G, = S, and S, = S, = 0. Therefore, the total network load G, an be written as Hene, S, = G, and S, = S, = 0 in the range Gd 5 G, 5 G,. Using the results derived above, the offered load vs throughput harateristis an be summarized as follows: Region 1 : 0 5 G, 5 G, S, = G,, i = 1,2,3. (38) Region 2 : G, 5 G, 5 Gb S, = G,, i = 1,2 and (39) In this region, the throughput of lass 3 is found using linear interpolation; for G, = G,, S, = Q, U, where U, is given by Equation (15) and for G, = G,, S, = 0. Region 3 : G, 5 G, 5 G, S, = G,, i = 1,2 and S, = 0. (40) Region 4 : G, 5 G, 5 G, S,=G,, i=l, S, = a, U, for G, = G, where U2 is given by Equation (29) and S, = 0 for G, = Gd. In this region, the throughput of lass 2 is found using linear interpolation. Region 5 : G, _< G, 5 G, S, = G,, i =1 and S, =S, = O. Region 6 : G, 5 G, S, = a, U,, : = 1 and S, = S, = 0, and U, in Equation (43) is given by Equation (36). (42) (43) This analysis is true only if the ondition given by Equation (2) is satisfied. Throughput harateristis depend on the relationship between the threshold values of different lasses. For example, onsider threshold settings satisfying the relationship, TTRT > T-Pri(2) > T-Pri(l) > T-Pri(3). (44) For this ase, we have to onsider two possibilities. 1. Final lass 2 throughput is higher than the lass 1 throughput S, > S, 2. Final lass 1 throughput is higher than the lass 2 throughput S, > S, 1001

6 For either possibility, we an derive similar expressions for C and the utilization as before. A detailed model overing all the possibilities is being developed [17]. IV. Parameter Seletion of FDDI Network The bandwidth requirement for a single voie onversation is a very small fration of the bandwidth of FDDI. Therefore, in order to provide a substantial voie load to the network, more than one voie hannel per station is allowed in the model. This way, when the station aptures the token, it is allowed to transmit one voie paket from eah hannel. Let the number of voie hannels per station be f. Lets assume that voie pakets of length L, is generated at fixed time intervals of P, in all voie hannels per station after sampling, quantization and a possible text ompression. The total voie load of the network Go is given by, The high-priority-token-time T, is thus given by, (45) The mean number of time units required to transmit voie pakets during a yle Tsv, and the mean number of time units available for asynhronous traffi during a yle Tasyn are given by, Tsr, = N,. T,, (47) Taw = TTRT - Tsun - CO. (48) To provide a steady throughput for asynhronous traffi, > 0. This TaSv is dynamially alloated among all stations whih support asynhronous traffi. The FDDI protool guarantees a worst ase aess delay of 2 TTRT and a mean aess delay of TTRT for synhronous traffi at a station [NI. Therefore, if TTRT is % P,, then synhronous traffi will have the above bounded delays. The values for T-Pri(i) for i = 1,2,3 depends on the partiular appliation. Nevertheless T-Pri( :) annot exeed the value of TTRT. The largest value assigned for any T-Pri(i) has a signifiant effet on the asynhronous over-run problem [HI. The synhronous traffi transmission is stritly limited to the duration of T, after a station aptures the token. The asynhronous message transmission is governed by a different set of rules. One a station begins to transmit a message from an asynhronous priority lass i, it is allowed to omplete the transmission of this message even when the THT exeeds the respetive lass threshold T-Pri(i). Due to this over-run of asynhronous messages, the TRT of ertain stations downstream of the ring an exeed the maximum token-yle time ( 2 TTRT). Aording to FDDI protool, this is a protool violation and ring reovery proedure(s) must be initiated [19]. It is very diffiult to avoid this protool violation if the largest value of T-Pn(i) is equal to TTRT. Therefore, we have assigned the largest value of any T-Pri(i) to be at least several message lengths less than TTRT. This riteria does not guarantee a permanent solution for the protool violation of the ring. This riteria of seleting the largest value for any T-Pn (i) gives satisfatory results for low load or moderately high load onditions. Some other forms of solutions for asynhronous over-run problem are given in [18]. As the model presented in Setion 111 is based on mean value analysis, it provides aurate results only when the values assigned for the T-Pri(i)s are at least several message lengths apart from eah other. If two or more T-Pn(i)s have equal or very lose values, the model annot be used evaluate the individual lass throughput. Instead, it an be used to find the total throughput of the two or more lass& that have equal or approximately equal values for their respetive T-Pri(i)s. Although we do not provide a parameter tuning proedure for T-Pri(i) as given in [13], our analytial model an be used to find a set of suitable values for T-Pn(r)s to math the desired harateristis for the given appliation. V. Results In this setion, we present a omparison of the results obtained from the analytial model desribed in Setion 111 with the results obtained via a omputer simulation model. The timer values and parameters for both models are alulated aording to the desription given in Setion IV. The asynhronous load at a station is arbitrarily assumed to be distributed among the lasses 1, 2 and 3 aording to the ratio of 3:2:1. Length of voie pakets is 3200 bits, and are generated at 50 mse time intervals in eah hannel. From Equation (45), it an be shown that for N, = 79 voie stations, 2 voie hannels per station are required to generate a Go = 10% voie load for the network. When it is neessary to raise the voie load, the number of voie hannels allowed at a station is inreased. A total of 200 stations are onsidered with 50 voie only stations, 29 voie and data stations, and the rest being data only stations. The stations are assumed to be evenly spaed in a 20 km fiber path with a propagation delay of 5.09 pse/km and a station lateny of 0.6 pe/station. All stations supporting voie traffi are assumed to have idential statistis for voie message generation. The data messages follow Poisson arrivals, and the length is assumed to be exponentially distributed with a mean of 2048 bits. 160 overhead bits are added to eah message before transmission. The token-apture time is negleted in the analytial model, but is taken into aount in the simulation model. The network timer and parameter values are omputed as desribed in the Setion IV based on the values seleted above. A summary of all the values used are given in Table 11. The offered load vs throughput harateristis for a 10% voie load is illustrated in Figure 3. The network is able to transmit all of lass 0 messages even when network is over TTRT (bit times) 3200 (bits) (bit times) I T, xf (bit times) I Table II: Network parameters used for performane analysis 1002

7 ~~ i.2 C.5 Analytial L." L" S - 0- : L 0.5 k - i a.! H e 0.3 r F 0.2 Analytial Simulation Class 0 X Class I 0 Class 2 V Class 3 5 x 0.1 CF'ZZEZ ici2 G Figure 3. Throughput of lass i vs. total offered load (i=0,1,2,3) for 10% voie load. 0.0 I ' 1-2.E U, C.i Simulation Class 0 X Class I i.3- J s Analytial / imulation l i d / i -+- C.5 C.2 Class 3 x Ix. I li O.! C.0 1.s 2.3 t o n. G.5.._I.._I CF-ZiE? CF-ZZE?,ZFO LZFO 6 Figure 4. Throughput of lass i vs. total offered load (i=0,1,2,3) for 30% voie load. -." 0.D C : CF-L:EI LtF: G Figure 6. Mean message delay of lass i vs. total offered load (i=0,1,2,3) for 30% voie load. loaded. Figures 4 and 5 illustrate the offered load vs throughput harateristis for 30% and 50% voie loads respetively. Note that, when the voie load is raised from 10% to SO%, there is a onsiderable redution in the throughput of all asynhronous lasses sine the bandwidth alloation for asynhronous traffi is redued. The simulation results for all the ases onfirm the results provided by the analytial model. At high loads, only lasses 0 and 1 sustain a non-zero throughput due to the restrition imposed by Equation 2. For a 30% voie load, the aess delay of various lasses is shown in Figure 6. Note that, the aess delay of lass 0 inrease from 5 mse to 18 mse when the total network load is inreased from 30% to 200%. The aess delay of lass 0 at higher loads is 12 and 19 mse for 10% and 50% voie loads respetively. These results show the apability of the FDDI network to deliver its synhronous lass messages with a predetermined aess delay. Due to the assumption of infinite buffer apaity, the aess delay of asynhronous lasses 1, 2 and 3 beome infinitely large one the offered load exeeds the maximum throughput of the respetive lass. Finally, our results show that FDDI network an support 158 simultaneous.voie onversations when the voie load is a mere 10%. This an be raised up to 790 simultaneous onversations when the voie load is 50%. The throughput of asynhronous lasses are drastially redued with the inreasing voie load. From mean message delay harateristis, it an also be onluded that no voie pakets are lost or disarded due to exessive delays. The model results are verified using the results obtained from an event-driven simulator written in FORTRAN. Main program utilizes several subroutine alls for message generation, message transmission, token propagation, statistial data olletion and to update loks and event list. The initial statistial data of the network is disarded and the data used for model verifiation are olleted after the network has reahed steady state. For eah parameter/variable of interest, four sample values are alulated in four onseutive equal time intervals. The sample mean is used as the estimate of the parameter. The popular 95% onfidane interval is alulated using t-distribution and is given by, ( X, - t(n - l]u,/g, X, + t(n - 1)nJG ), where n is the number of samples and X, and us are the mean and the standard deviation of the samples respetively. For n =4, from t-distribution tables, t(3)= In Figure 6, the lass 2 messages at 92% total load has the worst ase onfidane interval 1003

8 at (13.59J6.38) mse with a sample mean of mse. Hene, the variation of sample mean for mean message delay is less than or equal to f1.4 mse. VI. Conlusion Performane of a non-homogeneous FDDI token-passing ring network has been evaluated in the presene of both synhronous and asynhronous traffi. The results show that the model presented an aurately predit the throughput harateristis. A sheme has been proposed to alulate the network parameters to meet the desired performane requirements. Sine, the omputer simulation models onsume a large amount of CPU time, the analytial model provides an effiient way to alulate the throughputs of all the lasses with high auray. It an also be used to alulate the lass threshold values T-Pri(i) to obtain the desired throughputs. The analytial model has been derived under the assumption that the network is non-homogeneous. The model assumes that there is at least one voie and data station and one data only station. A model an be developed for the ase where no suh stations exists, using similar arguments [15]. In order to use the model to evaluate the throughput of individual lasses of priorities, the respetive lass thresholds T-Pri(i)s should differ at least by several message lengths. Otherwise, the model an be used to evaluate the ombined throughput of two or more lasses that have equal or approximately equal T-Pri(a)s. Further, this model is valid only if the ondition TTRT > T-Pri(l) >T_Pri(2) > T-Pri(3) is satisfied. However, this model an easily be extended to over other possibilities suh as TTRT > T-Pri(2) > T-Pn(1) > T-Pn(3) [17]. The results presented here an also be extended to predit the performane of IEEE token-bus priority sheme under similar onditions. Referenes 1. FDDI Token Ring Media Aess Control (MAC), Draft Proposed Amerian National Standards, X3T9.5/83-16, Rev 28, Feb FDDI Station Management (SMT), Draft Proposed Amerian National Standards, X3T9.5/84-49, Rev 2.1, April A. P. Jayasumana, Performane Analysis of a Token Bus Priority Sheme, Pro. IEEE INFOCOM, pp 46-54, Marh A. P. Jayasumana, and P. D. Fisher, Performane Modeling of IEEE Token Bus, Pro. IEEE-NBS Workshop on Fatory Communiations, pp , Marh A. P. Jayasumana and G. G. Jayasumana, Simulation and Performane Evaluation of Priority Sheme, Pro. IEEE-ACM Sympoaium on the Simulation of Computer Networks, pp , August A. P. Jayasumana, Throughput Analysis of IEEE Priority Sheme, IEEE Trans. Communiations, Vol.Com-37, No-6, pp , June W. L. Genter and K. S. Vastola, Performane of High Priority Traffi on a Token Bus Network, Pro. 27th IEEE Conf. on Deision and Control, Austin, Texas, Deember A. P. Jayasumana and G. G. Jayasumana, On The Use of The IEEE Token Bus in Distributed Real-Time Control Systems, IEEE Trans. Industrial Eletronis, Vol. 36, No. 3, August W. L. Genter and K. S. Vastola, Performane of The Token Bus for Time Critial Messages in a Manufaturing Environment, Pro Amerian Control Conf., June S. Ayandeh, Performane of the IEEE Token Bus Protool for Distributed Real-Time Appliations, to be presented at INFOCOM J. W. M. Pang and F. A. Tobagi, Throughput Analysis of a Timer Controlled Token Passing Protool Under Heavy Load, IEEE Trans. Communiations, VoI.Com37, No-7, pp , July J. M. Ulm, A Timed Token Protool for Loal Area Networks and Its Performane Charateristis, Pro. IEEE 7th Loal Computer Networks Conf., pp 5C-56, February D. Dykeman and W. Bux, Analysis and Timing of the FDDI Media Aess Control Protool, IEEE Seleted Areas in Comm., Vol 6, No.6, pp , July M. Fontini and G. Watson, An Investigation of Paketized Voie on the FDDI Token Ring, Pro Int. Zurih Sem. on Digital Commun., B. Plattner and P. Gunzburger, Eds., pp A. Goyal and D. Dim, Performane of Priority Protools on High-speed Token Ring Networks, Pro. 3rd Int. Conf. on Data Communiation Systems and Their Performane (Rio de Janeiro, Brazil), L. F. M. de Moreas, E. de Souza e Silva, and L. F. G. Soares, Eds. Elsevier B.V. (North-Holland) IFIP 1988, June 1987, pp A. Valenzano, P. Montushi and L. Ciminiera, On The Behavior of Control Token Protools with Asynhronous and Synhronous Traffi, Pro. IEEE INFOCOM, April 1989, pp P. Werahera and A. P. Jayasumana, Performane Evaluation of FDDI networks, Tehnial Report (under preparation), Dept. of Eletrial Engineering, Colorado State University. 18. K. C. Sevik and M. J. Johnson, Cyle Time Properties of The FDDI Token-Ring Protool, J.ACM Proeedings of Performane 86 and ACM Sigmetris 1986, 27, North Carolina State University, May M. J. Johnson, Proof That Timing Requirements of FDDI Token Ring Protool are Satisfied, IEEE Trans. Communiations, Vol.Com-35, pp , June I004