On the GI/M/1/N queue with multiple working vacations—analytic analysis and computation

AbstractWe consider finite buffer single server GI/M/1 queue with exhaustive service discipline and multiple working vacations. Service times during a service period, service times during a vacation period and vacation times are exponentially distributed random variables. System size distributions at pre-arrival and arbitrary epoch with some important performance measures such as, probability of blocking, mean waiting time in the system etc. have been obtained. The model has potential application in the area of communication network, computer systems etc. where a single channel is allotted for more than one source

Computing queue length and waiting timedistributions in finite-buffer discrete-time multiserver queues with late and early arrivals

AbstractThis paper presents modelling and analysis of discrete-time multiserver finite-buffer queue with general interarrival and geometric service time. Using the supplementary variable technique, and considering the remaining interarrival time as a supplementary variable, two variants of this model, namely the late arrival system with delayed access (LAS-DA) and early arrival system (EAS), have been examined. For both the cases, steady-state system length distributions at arbitrary, prearrival, and outside observer's observation epochs have been obtained. Further, the waiting time distribution in the queue is also discussed. Various performance measures such as probability of loss, average number of busy servers and average waiting time in the queue etc. have been presented. It is hoped that the results obtained in this paper may provide useful information to designers of telecommunication systems, practitioners, and others

A batch-service queueing model with a discrete batch Markovian arrival process

Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of customers in system (system content) reaches or exceeds a threshold. Correlation is taken into account by assuming a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. We deduce the probability generating function of the system content at random slot marks and we examine the influence of correlation in the arrival process on the behavior of the system. We show that correlation merely has a small impact on the threshold that minimizes the mean system content. In addition, we demonstrate that correlation might have a significant influence on the system content and therefore has to be included in the model

Multi-color Optical Variability of the TeV Blazar Mrk 501 in the Low-State

We report results based on the monitoring of the BL Lac object Mrk 501 in the optical (B, V and R) passbands from March to May 2000. Observations spread over 12 nights were carried out using 1.2 meter Mount Abu Telescope, India and 61 cm Telescope at Sobaeksan Astronomy Observatory, South Korea. The aim is to study the intra-day variability (IDV), short term variability and color variability in the low state of the source. We have detected flux variation of 0.05 mag in the R-band in time scale of 15 min in one night. In the B and V passbands, we have less data points and it is difficult to infer any IDVs. Short term flux variations are also observed in the V and R bands during the observing run. No significant variation in color (B$-$R) has been detected but (V$-$R) shows variation during the present observing run. Assuming the shortest observed time scale of variability (15 min) to represent the disk instability or pulsation at a distance of 5 Schwarschild radii from the black hole (BH), mass of the central BH is estimated $\sim$ 1.20 $\times$ 10$^{8} M_{\odot}$.Comment: 4 figures, 4 tables, Accepted for publication in New Astronom