Analysis of queueing systems with reneging customers and server failures

Abstract

In queueing systems, customers may leave the system without service or the server may be subject to deterioration and failures. This dissertation considers the concept of "negative customer", "disaster", and "random shock" to model queues with reneging customers and server failures. First, we extend the queueing theory on negative customers to GI/M/1 queues. When a negative customer arrives at the system, it immediately removes a customer. A negative customer is a kind of work cancellation. We consider FIFO and preemptive LIFO service discipline. The system size distribution and the sojourn time distribution are derived. Second, we analyze M/G/1 queues with disasters. In these systems, an external arrival of a disaster removes all workload in the system. We can think of the disaster as a machine breakdown that causes all the jobs in the system to be lost. We present the system size distribution and the sojourn time distribution. Finally, we propose a random review replacement policy of single server queues with random shocks that cause deterioration and breakdowns of a server. Shocks deteriorate the effectiveness of a server. A repairman monitors the system randomly and replaces the server instantaneously if the cumulative magnitude of shocks exceeds a maintenance level. We analyze the system size distribution and the sojourn time distribution. An efficient algorithm for computing the sojourn time distribution function is derived. A cost analysis is performed to investigate the optimal maintenance level.``