To handle more phone and personal computer users in such a natural disaster as terribly strong earthquake, a traffic control has been previously proposed by limiting the individual call holding time. This traffic control mechanism leads to our T-limited service. By T-limited service, we mean that the service time is limited to a threshold T. The call whose service time reaches T is assumed to be lost. For evaluating the traffic control performance, we present multi-server loss systems with T-limited service. Without any retrial queues, we analyze a Poisson input and general service time loss system to derive the steady-state distribution of the number of calls in the system. With a retrial queue, assuming further that the call sojourn time at the retrial queue is exponentially distributed and that the T-limited service time is also exponentially distributed, we propose an approximation for the steady-state distribution of the number of calls in the system. Our approximation accuracy is validated by a simulation result.

Although diffusion approximations are widely used for analyzing non-Markovian queueing systems, so far there are few results on the relationship between the approximation accuracy and a combination choice of two boundary conditions and two discretization for finite-capacity multi-server queuing systems. The finite-capacity system requires two boundary conditions at origin (x=0) and capacity limit (x=K). Taking account of this requirement, four types of diffusion approximations have been presented. We present accuracy comparisons among four types of diffusion approximations which differ from one another in the boundary conditions and the discretizations. We observe that the coefficient of variation of the inter-arrival time distribution is a key factor for choosing the appropriate combination of the boundary conditions and the discretizations.

A doubly stochastic point process is proposed and analyzed. It is a switched batch Bernoulli process (SBBP) for modeling bursty and correlated input to discrete-time queuing systems. Through the investigation of the counting process, statistical characterization measures of the SBBP are explicitly obtained. A discrete-time single-server queue with SBBP input and general service time (SBBP/G/1) is then considered. The SBBP/G/1 queue has a potential applicability to a statistical multiplexer in the network. The supplementary variable technique is used to obtain the probability generating functions of performance measures in the SBBP/G/1 queue. It is shown how the SBBP is suitable for analyzing a discrete-time queue with bursty and correlated input.>