A Markovian queue with varying number of servers and applications to the performance comparison of HSDPA user equipment

Inspired by the need for performability models for HSDPA user equipment, a Markovian queue with varying number of servers is conceived. The arrival and the service processes, the number of allocated or active servers of the queue are inherently, and independently (or jointly) Markov modulated. Batch arrivals, batch services, autocorrelation of inter-arrival times, and autocorrelation of batch sizes can be accommodated in the queue, by a suitable use of Markov modulation and generalized exponential distribution. The queue has a provision for negative customers too. Transformations of the balance equations into a computable form are proposed in order to obtain the steady state probabilities with the Spectral Expansion method. This queue is used to model the High Speed Downlink Packet Access (HSDPA) wireless networks. The model is an integrated one with respect to HSDPA, capable of accommodating many of the intricate aspects of HSDPA such as, channel allocation policy, loss of packets due to channel fading, bursty and correlated traffic. Good agreement is observed between the numerical results of the proposed analytical model and those of an independent simulator of real HSDPA and radio channel behaviors. The comparison of the terminal categories specified by the 3rd Generation Partnership Project (3GPP) is also presented.