Computing packet loss probabilities of D-BMAP/PH/1/N queues with group services

Statistical multiplexers have been integral components of packet switches and routers on data networks. They are modeled as queueing systems with a finite buffer space, served by one or more transmission links of fixed or varying capacity. The service structure typically admits packets of multiple sources on a first-come first-serve (FCFS) basis. In this paper, we adhere to D-BMAP/PH/1/N queues with discrete phase-type group service channel which allows the packets to get service in the service channel for a random number of time slots by staying in different phases of the service channel before they leave the switch. The aim is to determine the packet loss probability (PLP) as a function of the capacity of the buffer. Due to the curse of dimensionality of the mathematical model, the numerical computation of the performance measures using the analytical formulas is time and memory consuming. Due to rare events, getting the performance measures by simulation is again time consuming. To overcome this problem, we use the Newton–Padé-type rational approximation technique to compute the PLP more efficiently. Since this technique needs the asymptotic behavior of the PLP, we show a way to regroup the elements of the TPM to obtain the asymptotic behavior of the PLP.