Analysis of random polling system with an infinite number of coupled servers and correlated input process

Abstract

We introduce a simple approach for modeling and analyzing a random polling system with infinite servers. We assume that the infinite number of servers is coupled together and they visit the queues as one processing unit. It is assumed that the customer arrival processes at all queues are correlated. Two classes of service disciplines, exhaustive and gated, are considered. We will derive several performance measures of the system. These performance measures include the mean cycle time and the expected delay observed by a customer. For the special case of M/ D/∞ vacation queue, we also provide a new proof of a known result. The numerical results indicate that when the expected number of busy servers is high gated service produces mean waiting times less than those given by exhaustive service discipline. This result differs significantly from the known result for single server polling system and it is due to the assumption of coupled servers. Scope and purpose The Information Community's insatiable appetite for timely information has led to a number of new services: voice, data, teleconferencing, entertainment video, local area networks bridging, and distributed data processing. For both economic reasons and sophistication of services provided, a multicast feature must be provided. An essential component of multicasting is communication link sharing, an example of which is a self-routing network. Furthermore, the dramatic increase in transmission speed due to advancing technology has significantly altered many of the operating assumptions of communication systems. In particular, the quality of services provided by these communication systems can be improved by redesigning the access control mechanisms. Thus, the design and analysis of high-speed communication networks is drawing increasing attention. As a result, a number of approaches has been proposed for controlling the high-speed communication systems typified by parallel communication in fixed time synchronous mode. The parallel communication aspect is a result of advancing technology. For example, widespread use of fiber optics in parallel buses, parallel rings and star topology networks using frequency or wavelength division multiplexing have made high-speed parallel communication a reality. Furthermore, it has been demonstrated that by using parallel high-speed communication systems the total system capacity can be increased beyond that given by the single channel high-speed communication system. The use of fixed synchronous time division control in high-speed parallel communication systems is dictated by the speed limitations of electronics. However, the implementation of fixed synchronous time division control in high-speed parallel communication systems at fiber optics communication rates has been shown to be feasible. Although a number of performance studies on parallel high-speed communication systems has appeared in the literature; the performance of parallel high-speed communication system is not well understood. Therefore, there is a need to develop models of parallel high-speed communication systems that enable one to analyze their performance. Furthermore, from the perspectives of design and control of the communication system, there is a need for medium access control protocols that will allow designers to prioritize the different stations and thus improve the overall system performance. Motivated by these observations, the objective of this paper is to introduce a new approach to modeling and analyzing parallel high-speed communication systems.