Response Time Distribution in a Tandem Pair of Queues with Batch Processing

Response time density is obtained in a tandem pair of Markovian queues with both batch arrivals and departures. The method uses conditional forward reversed node sojourn times derives the Laplace transform response probability function case that sizes are finite. result derived by generating takes into account path not overtake-free sense tagged task being tracked affected later at second queue. A novel aspect vector functions solved for, rather than single scalar-valued function, which requires investigation singularities certain matrix. recurrence formula to obtain arbitrary moments differentiation origin, these can be computed rapidly iteration. Numerical results for first four displayed some sample networks have product-form solutions their equilibrium queue length probabilities, along densities themselves numerical inversion transform. Corresponding approximations also (non-product-form) pairs “raw” batch-queues—with no special arrivals—and validated against regenerative simulation, indicates good accuracy. methods appropriate modeling bursty internet cloud traffic possible role energy-saving considered.