Queues with Batch Departures I

Departures from Many Queues in Series

We consider a series of n single-server queues, each with unlimited waiting space and the first-in first-out service discipline. Initially, the system is empty; then k customers are placed in the first queue. The service times of all the customers at all the queues are i.i.d. with a general distribution. We are interested in the time D(k, n) required for all k customers to complete service from...

Numerical analysis of queues with batch arrivals

A New Iterative Method for Systems with Batch Arrivals and Batch Departures

The asymptotic variance of departures in critically loaded queues

We consider the asymptotic variance of the departure counting processD(t) of the GI/G/1 queue;D(t) denotes the number of departures up to time t. We focus on the case that the system load % equals 1, and prove that the asymptotic variance rate satisfies lim t→∞ VarD(t) t = λ ( 1− 2 π )( ca + c 2 s ) , where λ is the arrival rate and ca, cs are squared coefficients of variation of the inter-arri...

Optimal Control of Parallel Queues with Batch Service

We consider the problem of dynamic allocation of a single server with batch processing capability to a set of parallel queues+ Jobs from different classes cannot be processed together in the same batch+ The arrival processes are mutually independent Poisson flows with equal rates+ Batches have independent and identically distributed exponentially distributed service times, independent of the ba...