Abstract

In this paper, we consider renewal arrivals to a communication link with s channels under both a loss system and a finite waiting room system. We assume that such a request arriving to this system holds a channel for exponentially distributed service time. For example, overflow traffic in a teletraffic network, or traffic that is bursty in data networks are non-Poissonian. We characterize renewal arrival by a matrix-exponential distribution (one with a rational Laplace transform). Performance measures of interest for the loss system are the call and time blocking, and for the finite waiting room system the call/time blocking and the average waiting time. Using linear algebraic techniques, we present steady-state balance equations and then describe efficient methods to exactly compute both call and time blocking for both the loss system and the finite-waiting room system. For the loss system, we present numerical results for various distributions considered for the arrival process and compare these with approximations such as Hayward's approximation. For the finite waiting room system, we present results on different sizes of the waiting room and provide comparison with Whitt's approximation. We also discuss results for renewal arrival to a link with buffering in a statistical multiplexing mode. Furthermore, we present results to show that depending on the value of s and the load offered to the system, the third moment of the arrival process may need to be considered for various performance measures.

To obtain a PDF file of this paper, click here . This PDF file is about 195K bytes.

To obtain a post-script file of this paper, click here . This PS file is about 515K bytes.