Stochastic Loss Systems: Models and Policies

Abstract

In a multi-server system, probability distributions and loss probabilities for customers arriving with k different priority categories are studied. Customers arrive in independent Poisson streams and their service times are exponentially distributed, with different rate for different priority. The non-queuing customers or the loss customers will be lost if the capacity is fully occupied. In these systems, particularly for higher priority customer the reduction of the loss probabilities is very essential to guarantee the quality of the service. Four different policies for k=2, high (emergency) and low (ordinary), were introduced utilising the fixed capacity of the system, producing different loss probabilities, by which the minimum can be selected. An example illustrating these results is also given.

Keywords: Cut off priorities, Loss probabilities, Multi- Server, Stochastic models, Steady State.

2000 Mathematics Subject Classification. Primary: 60K25, Secondary: 60K15, 90B10