On Discretionary Priority Queueing

Abstract

Abstract A priority regime is envisaged for single queuing systems composed of two customer populations with Poisson arrivals which is intermediate between the two extreme doctrines: a) head of the line priority, b) pre‐emptive priority. The state of intermediacy is represented by discretionary powers vested in the server to interrupt recently initiated ‐ and not to interrupt almost completed ‐ service to a low priority customer upon the arrival of a high priority customer. For the case of constant service times the discretionary rule is defined and the ensuing queueing characteristics analyzed; in particular, the average total queue lengths of both high and low priority customers are derived for two different cases: a) the resume situation where service renewed to a low priority customer starts at the point of interruption; b) the repeat situation where service given to a low priority customer before an interruption, is completely lost. Optimisation procedures are outlined and for the resume situation a simple optimal discretionary rule is obtained.