Risk Assessment of a Stochastic Service System

Abstract

A stochastic service system of finite size M is comprised of identical service facilities, including or not a waiting queue, which simultaneously treats N customers, N ∈ {0, 1, …, M}. Depending on the concepts of system information i and system entropy S = E(i), we promote a risk assessment procedure. By definition, the system entropy is the uncertainty associated with the system, and the system expected loss is the risk associated with the system. Thus, accepting the system information as loss function, we can identify risk and uncertainty, associated with the system, using the entropy as risk function. Further, we differ risk of the system (i.e., risk observed by an outside observer), risk observed by an arriving customer, and risk observed by a departing customer, giving a separate expression for each one. Then, these risks are compared with each other, when the system has the same average number E(N) of customers seen by any viewpoint. The three risk types (together with the three customer means) allow us to distinguish two systems obeying the same probability distribution. This approach enables system operators to choose suitable values for system utilization and size, in view of the three risks ratio. The developed procedure is applied to the information linear system, Erlang loss system, single-server queueing system with discouraged arrivals, Binomial system and Engset loss system.

Keywords

Absolute and relative risk / uncertainty / system information and entropy / system utilization / stochastic service system

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