R. V. Cox and R. E. Crochiere, âMultiple user variable rate coding for TASI and packet transmission systems,â IEEE Trans. Commun., vol. COM-28, pp. 33&337 ...
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-29, NO. 6 , JUNE 1981 voice flow control in integrated packet networks,” IEEE Trans. Commun., vol. COM-28, pp. 325-333, Mar. 1980.
R. V. Cox and R.E. Crochiere, “Multiple user variable rate coding for TASI and packet transmission systems,” IEEE Trans. Commun., vol. COM-28, pp. 33&337, Mar. 1980. 1351 D. J. Goodman, “Embedded DPCM for variable bit rate transmission,” in Int. Commun. Conf. Rec., vol. 3, Seattle, WA, June 1980, pp. 42.2.142.2.7. Also, IEEE Trans. Commun.. vol. COM-28, pp. 104C1046, July 1980. 1361 J. S. Dubpowski and R. E. Crochiere, “Variable rate coding of speech,” Bell Sysr. Tech. J . , vol. 58, pp. 557400, Mar. 1979. Also, in ICASSPRec., Washington, DC, Apr. 1979, pp. 445448. S . E. Youngberg, “Rate/pitch modification of speech usingthe constant Q transform,” in ICASSP Rec., Washington, DC, Apr. 1979, pp. 748-751. J:L. LoCicero and P. M. Bocci, “Entropy coding of ADM speech signals,” in Inr. Commun. Conf. Rec.. vol. 3, Seattle, WA, June 1980, pp. 42.7.1-42.7.5. D. Rubin, E. Ciaighill, and R. Rom, “Topics in the design of a natural teleconferencing system,” in Nut. Telecommun. Conf. Rec., vol. 1, Birmingham, AL, Dec. 3 4 , 1978. pp. 12.4.112.4.5. J. W. Forgie, “Voice conferencing in packet networks,” in Int. Commun, Conf. Rec., vol. 2, Seattle, WA, June 1980, pp. 21.3.121.3.4. G. J. Coviello and R. D. Rosner, “Cost considerations for a large data network,” in Int. Commun. Conf. Rec., Stockholm, Sweden, Aug. 1974, pp. 7-15-7-20. I. Gitman, B. Occhiogrosso, and W. Hsieh, “Sensitivity of integrated voice and data networks to traffic and design
variables,” in Proc. 6rh Dura Commun. Symp., Pacific Grove, CA, NOV. 1979, pp. 181-192. [ 1431 N. Janakiraman, “Performance analysis of multiplexers in circuit, packet and integrated switching environments,”Ph.D. dissertation, Dep. Syst. Eng. Comput. Sci., Carleton Univ., Ottawa, Canada, Aug. 1980. [ I 4 4 1 CCIR, Doc. 4/29-E “Proposed ammendment to annex to report 21 1-3: Speech interpolation technique in TDMA systems,” Japan, Jan. 1976. [I451 L. Kleinrock and F. Kamoun, “Hierarchical routing for large networks,” Compur. Nehvorks. vol. 1,’pp. 155-174, 1977.
* John G . Gruber is a native of Saskatchewan, Canada. He received the B.Sc. andthe M.Sc. degrees in electrical engineering from the University of Saskatchewan, Canada, in 1966 and 1969, respectively, and the Ph.D. degree in electrical engineering from Carleton University, Ottawa, Canada, in 1978. He joined Bell-Northern Research, Ottawa, Canada; in 1969, and, until 1975 he contributed to the development, analysis, and performance evaluation of high-speed digital transmission systems. He rejoined Bell-Northern in 1978, and has since been involved with telephony system planning and performance studies. His current fields of interest include the performance aspects of advanced switching techniques and of integrated services networks.
Performance Evaluation of a Variable Frame Multiplexer for Integrated Switched Networks BASIL MAGLARIS, MEMBER, IEEE, AND MISCHA SCHWARTZ,
Abstract-A scheme which multiplexes long messages and single messages, packetsusing a time-varyingframeispresented.Long generated from a fixed number of terminals, immediately access a main trunk, sharing a dynamically dedicated subchannel in a roundrobin fashion. Fixed size packets arrive with Poisson statistics in a FIFOqueueandareservedthroughthesametrunk, using the remaining capacity. The two traffic categories share an integrated variable length frame. The frame length is determinedby the volume of the increasing traffic at the beginning of the frame and cannot exceed a maximum value. Analysis of the performance of the system is carried out using finite MIGIN queueing populationround-robinprocessorsharingand techniques.Simplifyingmodelingassumptions are checkedwith simulation. A comparison with fixed frame schemes demonstrates the Paper approved by the Editor of Computer Communication for the IEEE Communications Society for publication after presentation at the MECO-78 International Conference, At$ens, Greece, June 1978. Manuscript received October 31, 1979; revised October 25, 1980. This work supported by the National Science Foundation under Grant ENG7808260. B. Maglaris was with theDepartment ofElectrical Engineering, Columbia University, New York, NY 10027. He is now with the Network Analysis Corporation, Great Neck, NY 11024. M. Schwartz is with the Department of Electrical Engineering and Computer Science, Columbia University, New York, NY 10027.
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I. INTRODUCTION ARIOUS techniques have been analyzed and implemented for multiplexing different data sendingfacilities over a large bandwidth channel. Message- or packetswitching techniques have been used for interactive short message traffic, resulting in efficient trunk utilization with small average time delay due to queueing. Lineswitchingis preferred for transmission of long messages with relatively small set-up time and full transparency [ 1] , [ 2 ] . Recently, emphasis has been placed onintegratedcommunication fadities capable of handling both long andshort message traffic. Most of the schemes assume a fixed time frame allocated statically or dynamically to both types of traffic. Ahalysis has shown that dynamic allocation results in a more efficient ;trqnk utdizationand smalldelays [3] -[5] . The advantageof dynamic allocation consists of using idle slots of &e line switching portion of a frame forpacket traffic while line switching keeps its full transparency in terms of proGding a pipeline type of service t o
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0090-6778/81/0600-0800$00.75 0 1981 IEEE
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MAGLARIS AND SCHWARTZ: EVALUATION O F VARIABLE FRAME MULTIPLEXER
the end users. Hardware problems and implementation are discussed extensively in a series of papers (see [ 6 ] , [7] , and
P I 1.
The full capacity of the main trunk is not used with fixed frame multiplexing schemes, since idle time slots occur when the overall traffic is sparse. Variable frame techniques, on the other hand, adjust the frame length in accordance with the variations of the traffic. Synchronization of line-switched customers now poses a problem resulting in nontransparent transmissions. It is, however, possible to bound the frame size to a certain maximum value admissible for transparency of circuit switching and, with thehelp of some buffering, realize integrated line and packet-switched systems with variable frame length. Such systems provide a savingsin bandwidth, but ?it the ttist of additional hardware and software complexity . Codex, Ftltporation has implemented arelated variable frame multiplexing system in its 6000 series network processors [9] . Under this scheme, dedicated time slots carrying no traffic are simply skipped. Fixed frame TDM line switching is thus replaGed with a statistical varying frame TDM scheme. Recendy, Miyahara and Hasegawahavesuggested in [lo] ari integrated switching scheme with variable “frame” and packet sizes: the outgoing trunk serves line switching “frames” with nonpreerliptive priority over conventional data packets. The “frami” is defined as the sequential collection of slots corresponding only to the line-switched traffic. Both the “frame” andthepacket sizes are restricted to certain maximum values. This system does not guarantee easyaccessof packets to the network,however, if the incoming line-switched traffic is dense and needs fast processing. “Frames” with priority over data packets would, in this case, monopolize the outgoing trunk. It would be useful to provide an analysis of variable frame switching systems, and, in particular, to compare their performance to those of the fixed frame type. This paper represents a step in that direction. In particular, we focus on a class of integrated, variable frame, multiplexing schemes in which a group of data terminals is each assigned a dedicated slot in the line-switched (LS) portion of a time frame; other user packets are servedin order of arrival in the packet-switched (PS) portion of the time frame. Note that by line switching we do not imply synchronous service. The terms line and packet switching are used to denote a dedicated uninterrupted service, versus a statistical multiplexing queueing discipline. The scheme proposed and analyzed in this paper is shown schematically in Fig. 1. The integrated frame shown, divided into an LS portion and a PS portion, may vary from a small delimiter value in case of no traffic present, to a maximum value corresponding to a heavy traffic case. The maximum frame length must not violate the line-switched transparency condition. (Equalizing buffers at the receiver should .be able to emulateasynchronous transmission withoutintroducing unacceptable latency.) To simplify the mathematical complexity and yet retain relevance to realistic environments, we choose as the LS model a group of terminals as noted earlier, permanently connected tothe multiplexer and served in round-robin fashion. This is similar to schemes proposed and
IDLE TERMINAL
BUSY
TERMINALS
INTEGRATEDFRAME
Fig. 1.
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implemented, which allow immediate access to a communications facility and dynamic sharing of the available capacity until completion of service. The Codex scheme, for example, scans users synchronously and serves them in a TDM fashion. But if no traffic is present, the dedicated TDM slot is skipped. The packet-switching submodel consists of a FIFO multiserver queue with Poisson arrivals and generalservice distribution. The service time is defined by the actual frame length, which, in turn, depends on the congestion state of both the LS and PS traffic. A detailed analysis of this queueing system appears in the Appendix. In Section 11,we introducethe detailed model of the system. We provide analyses for both the line-switched and the packet-switched traffic, leading to expressions for the average number of line-switched and packet-switched slots per frame and from these, the expected lineswitched transmission time and the average packet time delay. These last two parameters define the performance of the system. In Section 111 typical results are presented. The variable frame integrated switching scheme proposed here is compared in that section with a fixed frame movable boundary scheme.
11. THE MODEL AND ANALYSIS Acommunication line is considered shared by afinite population S of permanentlyconnected data sources (terminals) generating long messages of variable length and by a packet facility (e.g., infinitepopulation of bursty sources) sending packets of fixed length. The traffic isserved within a frame structure subdivided into two regions, one for each traffic class. The jth frame in time sequence consists of Si < slots of duration b and of N, < N slots of duration b’ (Fig. 2). The number Si represents the LS terminals actively transmitting at the beginning of the frame. In case an LS terminal is idle (called the “thinking” mode) during its time slot allocation, the slot is skipped and a delimiter set of bits (assumed negligiblein time duration) is used in its place. The number Ni represents the number of packets present in the packet queue at the beginning of the frame which are served during the frame period. Packet lengths are taken as the slot length b‘ in this model. The frame
s
accommodates all the packets in queue up to a maximum number N . The duration of.the frame will be
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