M/G/1 Queue with Multiple Working Vacations

We study an M/G/1 quene with muliple vacations and exhaustive service discipline such that the sever works with different service times rather than completely stops service a vacation. It is assumed that both service times in a vacation and in a service period are generally distributed randam variables. The length of a vacation is also generally distributed. We derive the distributions for the queue size and the system time for an arbitray customer in the steady state. Several special cases, namely, exponentially distributed vacation length and/or exponentially distributed service times in a vacation, are considered. Numerical examples are also presented.Includes bibliographical reference

Temperature dependence of the casein micelle structure in the range of 10–40 °C: an in-situ SAXS study

departmental bulletin pape

Multiserver queue with semi-Markovian batch arrivals with application to the MPEG frame sequence

We consider a queueing system consisting of multiple identical servers and a common queue. The service time follows an exponential distribution and the arrival process is governed by a semi-Markov process (SMP). The motivation to study the queueing system with SMP arrivals lies in that it can model the auto-correlatedtraffic on the high speed network generated by a real time communication, for example, the MPEG-encoded VBR video. Our analysis is based on the theory of piecewise Markov process. We first derive the distributions of the queue size andthe waiting time. The stability condition of the system is also discussed. When the sojourn time of SMP follows an exponential distribution all the unknown constants contained in the generating function of queue size can be determined through the zeros of the denominator for this generating function. Based on the result of the analysis, we propose a model to evaluate the waiting time of MPEG video trafficon an ATM network with multiple channels. Here, the SMP corresponds to the exact MPEG sequence of frames. Finally, a numerical example using a real video data is shown.Includes bibliographical reference

Reconsideration of a structural model of a casein micelle for small-angle X-ray scattering measurements

departmental bulletin pape