08/01/2000 09:00 AM
Computer Engineering
Queueing systems with priority service occur frequently in computer and other applications. For open M/G/1 queues with priorities, the exact solution for the expected time in queue is well known and easy to evaluate numerically. However, in many applications, the requests for service may come from a finite and possibly relatively small number of sources, so that a Poisson arrival process is not an adequate representation. Also, often, service is provided by a pool of servers so that a single server model is not valid. This is the case with multiprocessor CPUs in computer systems, as well as in machine interference systems with a team of operatives to repair failing machines of different priorities. In this paper, we consider systems with finite sources of requests, multiple servers and an arbitrary number of preemptive priority classes. The service times and the source idle times are assumed to be exponentially distributed. First, we analyze a system with fixed priorities i.e. we assume that each class of sources of requests correspondents to a distinct priority level. We present an efficient approximation method based on marginal state description. Our approach involves a recurrent analysis of priority levels, and we account for the usage of servers by higher priority requests through server \"vanishing\" and \"reappearance\" rates. This simple method produces generally satisfactory results, with occasionally more significant deviations from simulation results. An alternate method, which considers priority levels in pairs, appears to produce consistently accuate results. We then extend our approach to cases where sources can issue requests at several priority levels.
