IEEE TRANSACTIONS ON COMPUTERS, VOL. zyxwvutsrqpon 38, NO. zyxwvutsrqpon I, JULY 1989 1027 Approximate Analysis of Single and Multiple Ring Networks LAXMI N. BHUYAN, SENIOR MEMBER, IEEE, D I P M GHOSAL, MEMBER, IEEE, AND QING YANG, MEMBER, IEEE Abstract-Asynchronous packet-switched interconnection net- works with decentralized control are very appropriate for multiprocessing and data flow architectures. This paper presents performance models of single and multiple ring networks based on token ring, slotted ring, and register insertion ring protocols. The multiple ring networks have the advantages of being reliable, expandable, and cost effective. An approximate and uniform analysis, based on the gated M/G/l queueing model, has been developed to evaluate the performance of both existing single ring networks and the proposed multiple ring networks. Our approxi- mations are good for low and medium load. The analyses are based on symmetric ring structure with nonexhaustive service policy and infinite queue length at each station. They essentially involve modeling of queues with single and multiple walking servers. The results obtained from the analytical models are compared to those obtained from simulation. zyxwvutsrqp Index Terms-Distributed processing, multiple rings, packet- switched networks, performance analysis, queueing models, ring networks. I. INTRODUCTION NE of the important factors which limits the scalability of 0 parallel processing architectures is the interconnection network. As a result of this, a lot of research has been carried out on interconnection structures and, of late, interest has been focused on asynchronous packet-switched networks with decentralized control. The advantages of asynchronous packet-switched networks arise from two main reasons. First, synchronizing different devices in a large system has inherent difficulties, such as clock distribution and metastability prob- lems. The asynchronous control overcomes these problems and provides good system modularity and expandability zyxwvut . Second, the packet switching mechanism results in more efficient utilization of the interconnection network bandwidth. The notion of decentralized control of the interconnection network is one of the objectives of distributed processing because it provides graceful degradation in the event of failure. If all the requests are processed by a single network controller, the system speed is affected by the performance of the centralized controller. The centralized controller is also a major bottleneck from reliability considerations [5]. Thus, Manuscript received February 2, 1987; revised October 10, 1987. This work was supported by NSF Grant DMC-8513041 and by a grant from the Louisiana Board of Regents. L. zyxwvutsrqpon N. Bhuyan is with The Center for Advanced Computer Studies, University of Southwestern Louisiana, Lafayette, LA 70504. D. Ghosal is with the Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742. Q. Yang is with the Department of Electrical Engineering, University of Rhode Island, Kingston, RI 02881. IEEE Log Number 8928036. packet-switched interconnection networks with decentralized control are more appropriate for multiprocessing and data flow architectures [ 11, [9], [ 131, [201. Performance analysis of packet-switched multistage inter- connection networks (MIN’s) based on queueing models and through simulations have been reported in the literature [6], [13]. The major disadvantages of packet-switched MIN’s are that they are not modularly expandable and are complex to design. The multiple bus networks provide more expandabil- ity, modularity, and availability [ 11. Packet-switched multiple bus networks based on CSMA/CD type of decentralized bus access schemes have been studied [4], [18], [26]. However, due to the inherent nondeterministic nature of the CSMA/CD, the time to deliver a packet can become unbounded due to a large number of collisions and retransmissions. Ring networks are based on three well-known channel access schemes, namely, token ring, slotted ring, and register insertion ring. These have been widely used as local area networks both in commercial systems and research prototypes [ 161, [ 171. Ring networks offer several attractive features such as higher channel utilization and bounded delay with nonexhaustive service policy. However, the transmission delays faced by a message packet is high under moderate and high traffic loads. It is due to this high communication latency time that single ring networks are not well suited for distributed processing that requires high interprocessor com- munication. Providing high bandwidth through multiple rings is an attractive alternative because of cost and reliability considerations. Design issues of multiple rings for distributed processing have been reported in [8] and [27] and their protocols are briefly described in subsequent sections in this paper. Tagged token data flow architectures based on the multiple slotted ring network have been reported in the literature [9]. In this paper, we present performance models of both single and multiple symmetric ring networks for all the three channel access schemes. Our approach here has been to provide a simple, closed form, and unified analysis for these networks based on similar assumptions and protocols. The token ring local area network was first thoroughly analyzed by Konheim and Meister [ 121. In their analysis, they had assumed an exhaustive policy [16] whereby a station receiving a token uses the opportunity to transmit all messages waiting at the station before passing the token to the next station on the ring. Bux [2] and Tobagi and Kleinrock [23] adopted the basic model developed by Konheim and Meister. The model developed by Kuehn [ 141 assumes a nonexhaustive service of queues whereby a station can transmit only one 0018-9340/89/0700-1027$01.00 @ 1989 IEEE