Overload Performance of Several Processor Queueing Disciplines for the M/M/1 Queue

In a Variety of overloaded queueing systems (e.g., an overloaded call processing system), long delays can result either in poor service given to the customer or in customers, unknown to the system, turning "bad." For example, in switching systems, long dial tone delays can result in customers initiating dialing before receiving dial tone. In this case the system will not receive all the digits and an unsuccessful call results. This can lead to the system expending real time on unsuccessful services and, therefore, reduces the effective throughput. Thus, there is a need for control Schemes which reduce the load offered to the processor by selectively refusing service to some customers in such a way as to keep delays, for those customers which are selected for service, small. This fact has been recognized and has led to improved strategies for local switches. In this paper we analyze and compare the performance of various queueing and service disciplines for an queue. We consider LIFO and FIFO Schemes with customer rejection mechanisms corresponding to pushing out or timing out older customers in queue. Delay distributions for served customers are obtained and comparisons based upon throughput-delay tradeoffs are presented. For the situation where Customers can turn "bad" at a random time after their arrival, we compare the throughput of good customers. The results presented are a mixture of classical results, which are briefly stated, and new results which are developed in more detail. The numerical results show a dramatic effect of the queueing and Service disciplines on the overload performance and a strong dependence of the throughput of successful services on the mechanism for customers turning "bad." Although results are obtained for a single server queue, they can be used to approximately analyze overload control schemes which control access to distributed systems.