In ISDN and ATM, performance evaluation of packetized voice is an important problem. To analyse the superposed voice packets from a number of voice sources, the Markov modulated Poisson process (MMPP) has been used for approximating the superposed non-renewal process. In this approximation, a large computer time was needed for determining the MMPP parameters by the numerical inversion of Laplace transform. In this paper, introducing the index of skewness for counts as well as the index of dispersion, and using their conservation low, limiting property and differential coefficient at the origin, we propose a simplified method for determining the parameters.

This paper evaluates the performance of the statistical multiplexer with selective cell discarding (SCD) control in asynchronous transfer mode (ATM) networks. The multiplexer integrates delay-sensitive traffic such as voice or video and loss-sensitive traffic such as data, for which cell arrival processes are of bursty nature. The SCD control scheme is incorporated to prevent the systems from congestion as well as improve the system efficiency. It is based on the embedded ADPCM coding technology to packetize the delay-sensitive (voice & video) information into two kinds of cells: more significant part (MSP) cells and less significant part (LSP) cells, and priority is assigned to the MSP cells. When the system congestion occurs, the LSP cells are selectively discarded to reduce the congestion. In this paper, by approximating the two types of bursty inputs with respective Markov modulated Poisson processes (MMPP) and the fixed cell service time with k-Erlang distribution, we model the system under consideration as a queueing model MMP1[x]+MMPP2/Ek/1/m(m1), . Such a queueing model is analyzed by means of the matrix-analytic method, and the individual performance measures are derived. Numerical examples are shown to demonstrate the effectiveness of the SCD control scheme.

This paper presents an expanded numerical table for the coefficients of the asymptotic expansion for Erlang loss function and a formula for estimating the truncation error of the expansion. It is shown that the expansion gives a high accuracy for practical application ranges.

In recent communications systems, various kinds of traffic are transmitted all together. The mixed delay and non-delay system, which integrates loss-sensitive delay (data) traffic and delay-sensitive realtime (voice) traffic, is a typical example of these systems. In the mixed delay and non-delay systems, the non-delay traffic generally suffers loss with a relatively large probability due to the existence of the delay traffic. In order to improve the GOS (Grade of Service) of the non-delay traffic and to increase the efficiency of the overall systems, the alternative routing scheme is introduced. In design of the alternative routing systems, analysis of overflow traffic essential. This paper focuses on the moments of the number of the overflow calls from the mixed delay and non-delay systems with Poisson inputs and exponential service times. In the case of same mean service time, explicit formulas are presented for the moments, whereas a recursion formula and its calculating algorithm are derived in the case of different mean service times. Through the numerical results, a limiting property of the moments is discussed. An example is given to show the application of the obtained formulas.

This paper analyzes the delay performance of 1-persistent CSMA/CD LANs with bus topology and a finite number of heterogeneous stations, each possessing an infinite buffer. The mean waiting time at each individual station is obtained under a light-traffic assumption that the channel is occupied only by successful transmission periods. It is shown that the stations near the heavy-traffic stations gain better performance among light stations and the extent to which the individual delays differ depends on the network configuration as well as the protocol parameters.

The optimum design of alternative routing network systems applying the equivalent random theory, which minimizes the system cost under given service criteria, has been proposed for the basic triangular model. Practical networks, however, are more complex than this model; for example, the networks overflowing from an alternative route to a higher level one will be introduced. As a study of such networks, an approximate solution of the two-stage overflow model has been proposed, but its accuracy has not yet been made clear. This paper first investigates a general n-stage overflow model, and provides the optimum condition minimizing the system cost applying the implicit function theorem. Next, using the above result, the accuracy for the approximate solution of the two-stage model is evaluated numerically. Furthermore, a practical design for the two-stage system is proposed, which is based on the optimum design charts for the basic triangular model.

Consider the diffusion approximation for queues in randomly varying environment. The environmental variation may be the changes of arrival rates and/or changes of service rates caused by changes in message transmission under occasional crisis. The problem is to seek the queue size distribution conditional on the process being under different environment. The problem arises, for example, when we consider the delay distribution for each type of bursty customers in MG/G/1 queues, where MG represents nonhomogeneous renewal process GIi with i being two-state Markov process. To solve the problem, we define and analyze a diffusion process on R++R+ with the elementary returning boundaries. The forward equation and its stationary solutions are derived. Then it is applied to GI+IPP/G/1 queues and queues with service interruption, where IPP represents the interrupted Poisson process. Numerical examples are given in order to evaluate the accuracy of our approach. Finally a corrected diffusion parameter diminishing errors for general service time distributions is proposed.