A controlled M/G/1 workload process with an application to perishable inventory systems

Abstract

We derive the stationary distribution of the regenerative process W(t), t >= 0, whose cycles behave like an M/G/1 workload process terminating at the end of its first busy period or when it reaches or exceeds level 1, and restarting with some fixed workload alpha is an element of (0, 1). The result is used to obtain the overflow distribution of this controlled workload process; we derive Ee-(alpha W(T)) and E[e-(alpha W(T)) vertical bar W(T) >= 1], where T is the duration of the first cycle. W(t) can be linked to a certain perishable inventory model, and we use our results to determine the distribution of the duration of an empty period.