An Evaluation of Customer Delay in a Telecommunications Switchboard Subject to Two Types of Customer Demands.

摘要

A queueing system is investigated in which two types of customers, Type 1 and Type 2, attempt to access a multi-server operator switchboard. Customer arrivals for each type are assumed to be in accordance with independent Poisson processes with time constant parameters. Service times are assumed to be exponentially distributed and each type of customer has a different service rate. When a queue is formed, Type 1 customers are allowed to queue regardless of the length of the queue but Type 2 customers are blocked when the queue size exceeds a predesignated limit. An exact solution of the problem was not obtained and a discussion of the complications which precluded an exact solution is presented. A simulation algorithm is developed and validated by comparison with an exact solution of the special case of the problem in which the service rates are equal. Finally, an analytical approximation is developed and shown to give reasonable results by comparison with the simulation model. (Author)