De-An Wu

Bio: De-An Wu is an academic researcher from University of Tsukuba. The author has contributed to research in topics: M/G/1 queue & M/M/1 queue. The author has an hindex of 3, co-authored 5 publications receiving 220 citations.

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

Abstract: 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-correlated traffic 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 and the waiting time. 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 traffic on 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.

Processor-sharing and random-service queues with semi-Markovian arrivals

Abstract: We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-l customer who, upon his arrival, meets k customers already present in the SMP/M/1/PS queue is identical to the waiting time distribution of a type-l customer who, upon his arrival, meets k+1 customers already present in the SMP/M/1/RS queue. Two sets of system equations, one for the joint transform of the sojourn time and queue size distributions in the SMP/M/1/PS queue, and the other for the joint transform of the waiting time and queue size distributions in the SMP/M/1/RS queue, are derived. Using these equations, the mean sojourn time in the SMP/M/1/PS queue and the mean waiting time in the SMP/M/1/RS queue are obtained. We also consider a special case of the SMP in which the interarrival time distribution is determined only by the type of the customer who has most recently arrived. Numerical examples are also presented.

A Queue with Semi-Markovian Batch Plus Poisson Arrivals with Application to the MPEG Frame Sequence

Abstract: We consider a queueing system with a single server having a mixture of a semi-Markov process (SMP) and a Poisson process as the arrival process, where each SMP arrival contains a batch of customers. The service times are exponentially distributed. We derive the distributions of the queue length of both SMP and Poisson customers when the sojourn time distributions of the SMP have rational Laplace–Stieltjes transforms. We prove that the number of unknown constants contained in the generating function for the queue length distribution equals the number of zeros of the denominator of this generating function in the case where the sojourn times of the SMP follow exponential distributions. The linear independence of the equations generated by those zeros is discussed for the same case with additional assumption. The necessary and sufficient condition for the stability of the system is also analyzed. The distributions of the waiting times of both SMP and Poisson customers are derived. The results are applied to the case in which the SMP arrivals correspond to the exact sequence of Motion Picture Experts Group (MPEG) frames. Poisson arrivals are regarded as interfering traffic. In the numerical examples, the mean and variance of the waiting time of the ATM cells generated from the MPEG frames of real video data are evaluated.

Recent Developments in Vacation Queueing Models : A Short Survey

Abstract: Queueing systems with server vacations (server's performing non-queueing jobs) have been studied extensively since the late 70's. A considerable number of works in this area were completed in the early 80's and surveyed by Doshi in 1986. As an extension to the classical queueing system, allowing idle servers to work on non-queueing jobs makes the vacation models more applicable in a variety of systems including flexible manufacturing or service and computer communication systems. Motivated by these applications, more studies on vacation models have been done during the late 80's and 90's and surveyed in the book by Takagi in 1991 and the book by Tian and Zhang in 2006. This paper intends to provide a brief summary of the most recent research works on vacation queueing systems in the past 10 years. Keywords  server's vacation, batch arrivals, modified vacation policy, working vacations, multi-server vacation models.

The M/M/1 queue with working vacations and vacation interruptions

Abstract: In this paper, we study the M/M/1 queue with working vacations and vacation interruptions. The working vacation is introduced recently, during which the server can still provide service on the original ongoing work at a lower rate. Meanwhile, we introduce a new policy: the server can come back from the vacation to the normal working level once some indices of the system, such as the number of customers, achieve a certain value in the vacation period. The server may come back from the vacation without completing the vacation. Such policy is called vacation interruption. We connect the above mentioned two policies and assume that if there are customers in the system after a service completion during the vacation period, the server will come back to the normal working level. In terms of the quasi birth and death process and matrix-geometric solution method, we obtain the distributions and the stochastic decomposition structures for the number of customers and the waiting time and provide some indices of systems.