A Fluid Model for Many-Server Queues with Time-Varying Arrivals and Phase-Type Service Distribution

摘要

We introduce and analyze a deterministic fluid model that serves as an approximation for the G_t/PH/_(st) + GI many-server queueing model, which has a general time-varying arrival process (the G_t), a phase-type (PH) service distribution (the PH), a time-dependent number of servers (the s_t) and allows abandonment from queue according to a general abandonment distribution (the +GI). We provide an efficient algorithm, using matrix-analytic methods, to compute all standard transient (time-dependent) performance measures, such as the fluid content in queue, potential waiting time, abandonment and service-completion rate, etc.