A processor sharing model for wireless data communication

The use of loss models has a long history in the analysis of telecommunication networks, see e.g. the seminal book by Ross (1995). Typically, one model jobs that arrive at a loss station, with servers and request access to servers according to a Poisson process with rate $lambda$ and each job occupies these servers for an exponentially distributed holding time with mean $1/( mu)$. However, in lack of requested resources some Time Division Multiple Access (TDMA) implementations for mobile data communication like High Speed Circuit Switched Data (HSCSD) and General Packet Radio Service (GPRS) allow already established resources for data connections to be downgraded to allow a new connection to be established. As noted by Litjens and Boucherie (2002) this resembles classical processor sharing models, and in this spirit we formulate a variant of the processor sharing model with a limited and unevenly distributed number of allocated resources. The model is illustrated on a typical HSCSD setup. Performance characteristics, such as blocking probabilities, utilization, average allocated bandwitdh, sojourn- and response times are studied. The maximum likelihood principle is suggested for inferential purposes. c k k