The authors are interested in queuing models where the request arrival process exhibits significant deviations from a simple Poisson process. They say that state dependent arrival rates may be useful, for instance, to represent congestion avoidance in IP networks. Moreover, since any distribution can be approximated arbitrarily closely by a finite number of exponential phases, a possible approach is to use a phase-type distribution for the time between request arrivals. In this context they study the queuing model PH/M/c and its corresponding version with finite buffer, PH/M/c/N. For this last case they consider two different assumptions regarding the arrival process when the buffer is full: “lost arrivals” and “blocked arrivals”. The authors propose a semi- numerical approach to compute the steady-state probability distribution for the number of requests in the system both at arbitrary times and at instants of request arrivals. Leonardo Pasini
Mathematical Review of ( Brandwajn, Alexandre; Begin, Thomas -" A recurrent solution of PH/M/c/N-like and PH/M/c-like queues"- J.Appl.Probab. 49 (2012), no.1, 84–99. )
PASINI, Leonardo
2012-01-01
Abstract
The authors are interested in queuing models where the request arrival process exhibits significant deviations from a simple Poisson process. They say that state dependent arrival rates may be useful, for instance, to represent congestion avoidance in IP networks. Moreover, since any distribution can be approximated arbitrarily closely by a finite number of exponential phases, a possible approach is to use a phase-type distribution for the time between request arrivals. In this context they study the queuing model PH/M/c and its corresponding version with finite buffer, PH/M/c/N. For this last case they consider two different assumptions regarding the arrival process when the buffer is full: “lost arrivals” and “blocked arrivals”. The authors propose a semi- numerical approach to compute the steady-state probability distribution for the number of requests in the system both at arbitrary times and at instants of request arrivals. Leonardo PasiniI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
