A fluid approximation for large-scale service systems

We introduce and analyze a deterministic fluid model that serves as an approximation for the Gt/GI/st + GI manyserver queueing model, which has a general time-varying arrival process (the Gt), a general service-time distribution (the first GI), a time-dependent number of servers (the st) and allows abandonment from queue according to a general abandonment-time distribution (the +GI). This fluid model approximates the associated queueing system when the arrival rate and number of servers are both large. We also show that the system dynamics greatly simplifies in two special cases: (i) when the service time distribution is exponential (M) and (ii) when the service time distribution is deterministic (D) and the model is stationary. We develop an efficient algorithm to compute all standard performance functions in both cases. In case (i), we establish an asymptotic loss of memory (ALOM) property, i.e., asymptotic independence from the initial conditions as time evolves. We show that t...

• Type: Journal
• Year: 2010
• Where: SIGMETRICS
• Authors: Yunan Liu, Ward Whitt
• Keywords: Deterministic fluid Model, Hardware, Initial Condition, Model, SIGMETRICS 2010