Evaluating mean sojourn time estimates for the M/M/1 queue

AbstractMean sojourn time is one of the most important performance measures for queueing systems. It is difficult to obtain the real sojourn time of a customer directly, so it is also difficult to estimate the mean sojourn time. In this paper, we propose a new and relatively simple estimate of the mean sojourn time in a single server queue, using the number of arrivals and the number of departures. This method can be used for evaluating the quality and the performance of call processing in communication switching systems, for example. We evaluate the accuracy of this estimate for an M/M/1 queue, using some results obtained by Jenkins. This estimate is compared with two other standard estimates of the mean sojourn time obtained from the sequence of actual arrival and departure times

Dynamics of social queues

Queues formed by social wasps to inherit the dominant position in the nest are analyzed by using a transient quasi-birth-and-death (QBD) process. We show that the extended nest lifespan due to division of labor between queen and helpers has a big impact on nest productivity

Direct and indirect control of the initiation of meiotic recombination by DNA damage checkpoint mechanisms in budding yeast

Meiotic recombination plays an essential role in the proper segregation of chromosomes at meiosis I in many sexually reproducing organisms. Meiotic recombination is initiated by the scheduled formation of genome-wide DNA double-strand breaks (DSBs). The timing of DSB formation is strictly controlled because unscheduled DSB formation is detrimental to genome integrity. Here, we investigated the role of DNA damage checkpoint mechanisms in the control of meiotic DSB formation using budding yeast. By using recombination defective mutants in which meiotic DSBs are not repaired, the effect of DNA damage checkpoint mutations on DSB formation was evaluated. The Tel1 (ATM) pathway mainly responds to unresected DSB ends, thus the sae2 mutant background in which DSB ends remain intact was employed. On the other hand, the Mec1 (ATR) pathway is primarily used when DSB ends are resected, thus the rad51 dmc1 double mutant background was employed in which highly resected DSBs accumulate. In order to separate the effect caused by unscheduled cell cycle progression, which is often associated with DNA damage checkpoint defects, we also employed the ndt80 mutation which permanently arrests the meiotic cell cycle at prophase I. In the absence of Tel1, DSB formation was reduced in larger chromosomes (IV, VII, II and XI) whereas no significant reduction was found in smaller chromosomes (III and VI). On the other hand, the absence of Rad17 (a critical component of the ATR pathway) lead to an increase in DSB formation (chromosomes VII and II were tested). We propose that, within prophase I, the Tel1 pathway facilitates DSB formation, especially in bigger chromosomes, while the Mec1 pathway negatively regulates DSB formation. We also identified prophase I exit, which is under the control of the DNA damage checkpoint machinery, to be a critical event associated with down-regulating meiotic DSB formation

Budding Yeast Pch2, a Widely Conserved Meiotic Protein, Is Involved in the Initiation of Meiotic Recombination

Budding yeast Pch2 protein is a widely conserved meiosis-specific protein whose role is implicated in the control of formation and displacement of meiotic crossover events. In contrast to previous studies where the function of Pch2 was implicated in the steps after meiotic double-strand breaks (DSBs) are formed, we present evidence that Pch2 is involved in meiotic DSB formation, the initiation step of meiotic recombination. The reduction of DSB formation caused by the pch2 mutation is most prominent in the sae2 mutant background, whereas the impact remains mild in the rad51 dmc1 double mutant background. The DSB reduction is further pronounced when pch2 is combined with a hypomorphic allele of SPO11. Interestingly, the level of DSB reduction is highly variable between chromosomes, with minimal impact on small chromosomes VI and III. We propose a model in which Pch2 ensures efficient formation of meiotic DSBs which is necessary for igniting the subsequent meiotic checkpoint responses that lead to proper differentiation of meiotic recombinants

Evaluation of Breeding Strategies of Eusocial Species by Gene Extinction Probability (Theory of Biomathematics and Its Applications XVI -Toward quantitative understanding for life Sciences-)

Understanding eusociality in the view of Hamilton rule [1] is fundamentally important. Here, using a simple branching processes of gene propagation, we evaluate the extinction probability of genes in different cooperative breeding strategies of eusocial species [2, 3]. We discuss the relationship between the propagation advantage of breeding strategy and Hamilton rule

On the method of measurement and estimation of stochastic processes in communication

制度:新 ; 文部省報告番号:乙1362号 ; 学位の種類:博士(工学) ; 授与年月日:1998/3/5 ; 早大学位記番号:新2637 ; 理工学図書館請求番号:2235本文PDFは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルをPDFに変換したものである