| Abstract: | We consider the one-sided and the two-sided first-exit problem for a compound Poisson process with linear deterministic decrease between positive and negative jumps. This process (X(t)) t≥0 occurs as the workload process of a single-server queueing system with random workload removal, which we denote by M/G u /G d /1, where G u (G d ) stands for the distribution of the upward (downward) jumps; other applications are to cash management, dams, and several related fields. Under various conditions on G u and G d (assuming e.g. that one of them is hyperexponential, Erlang or Coxian), we derive the joint distribution of τ y =inf{t≥0|X(t)?(0,y)}, y>0, and X(τ y ) as well as that of T=inf{t≥0|X(t)≤0} and X(T). We also determine the distribution of sup{X(t)|0≤t≤T}. |
