Numerical Solution of Piecewise-Stationary Mt/Gt/1 Queues

We develop an algorithm for computing the (exact) cumulative distribution function of the time-dependent workload in a piecewise-stationary Mt/Gt/1 queue with a work-conserving service discipline and general service-time distributions, where service times are determined at arrival instants. The t subscripts indicate that the arrival rate and the general service-time distribution may change with time, but we allow changes only at finitely many time points. The algorithm is based on numerical transform inversion, using the classical Takacs double-transform of the transient workload in an M/G/1 queue recursively over the successive stationary intervals. In particular, we apply our recently developed Fourier-series-based inversion algorithms for two-dimensional transforms and nested one-dimensional transforms. We also do additional work to greatly speed up the computation while tightly controlling the error. As a consequence, the computation time grows only quadratically with the number of intervals. The algo...