Effect of Switchover Time in Cyclically Switched Systems

Abstract

Cyclic service queueing systems have a broad range of applications in communication systems. From legacy systems like the slotted ring networks and switching systems, to more recent ones like optical burst assembly, Ethernet over SDH/SONET mapping and traffic aggregation at the edge nodes, all may employ cyclic service as a means of providing fairness to incoming traffic. This would require the server to switch to the next traffic stream after serving one. This service can be exhaustive, in which all the packets in the queue are served before the server switches to the next queue, or non-exhaustive, in which the server serves just one packet (or in case of batch service, a group of packets) before switching to the next queue. Most of the study on systems with cyclic service has been performed on queues of unlimited size. Real systems always have finite buffers. In order to analyze real systems, we need to model queues with finite capacity. The analysis of such systems is among the most complicated as it is very difficult to obtain closed-form solutions to systems with finite capacity. An important parameter in cyclic service queueing systems with finite capacity is the switchover time, which is the time taken for the server to switch to a different queue after a service completion. This is especially true for non-exhaustive cyclic service systems, in which the server has to switch to the next queue after serving each packet. The switchover time is usually very small as compared to the service time, and is generally ignored during analysis. In such cases, the edge node can be modeled as a server, serving the various access nodes that can be modeled as queues in a cyclic manner. Hence, we assume that on finding an empty queue, the server will go to the next queue with a switchover rate of, say e, but if the queue is not empty, we ignore the switchover time and assume that the server will switch to the next queue with rate μ after serving one packet in the queue. While this generally led to quite accurate results in the past due to a large difference in ratios between the service and switchover times, this might not be the case today as optical communication systems are getting faster and faster. Thus the switchover time cannot always be safely ignored as smaller differences between switchover times and service times may introduce significant differences in the results. In order to analyze such systems, the switchover process can be modeled as another phase in the service process. The focus of this chapter is on the analysis of non-exhaustive cyclic service systems with finite capacity using state space modeling technique. A brief summary on the work done to date, in cyclic service systems is presented in Section 2, while some applications of such systems 6