General customer impatience in the queue <i>GI/G/</i>1

Abstract

For the queueing system GI/G /1 with both waiting-line and service-line customer impatience an integral equation for the limiting waiting-time distribution function W ( x ) is derived and the existence of W ( x ) proved when the system satisfies certain conditions. Two counter examples are constructed showing that W ( x ) does not necessarily exist. A sufficient condition for its existence in GI / G /1 with deterministic waiting-line impatience is given. Formal solutions for M / G /l are derived for deterministic impatience and negative exponential impatience.