Transient analysis of queueing system with two heterogeneous servers

Abstract

A method that uses an open-end diagram of queueing system functioning and relative probabilities is applied to study the queueing system with two heterogeneous servers, which is functioning within a given time period. According to the method a service process diagram is drawn. A feature of the method is the calculation of durations of the processes residual from the previous state. It allows describing in detail the functioning process of the queueing system for both infinite and finite time periods. The difference of the method from other approaches is the application of relations for computation of states without formulation and solution of any equations, absence of constraints on distribution of service time and inter-arrival time. The authors analysed the queueing system with arbitrary distributed service time and inter-arrival time, which is functioning within a random time period. Each state is characterized by idle time of devices or availability of the queue that allows, as a result, computing probabilities and average durations of idle time of servers, distribution of queue length, average time of stay in queue.