Distribution of number served during a busy period of GI/M/1/N queues-lattice path approach

Agarwal, Mukesh

doi:10.1016/s0378-3758(01)00148-3

Cited by 10 publications

(3 citation statements)

References 15 publications

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“…There is a single server who provides first phase of regular service (FRS) denoted by 1 ' ' S to all the units. As soon as FRS is complted, a unit may depart from the system with probability q (=1-p) (say) or at the end of the FRS some of them opt for a Second phase of optional service (SPS) denoted by 2 ' ' S with probability p (0 1) p ≤ ≤ .Further it is assumed that the services are given in the both the phases is nonpreemptive i.e. once selected for service (FRS or SPS), a unit is served to completion continuously.…”

Section: The Mathematical Modelmentioning

confidence: 99%

A Single Server Queueing System with Two Phases of Service and Vacations

Choudhury

2008

Quality Technology & Quantitative Management

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The single server queue with two phases of service with vacations has been extended to include several types of generalizations, to which attention has been paid recently by several researchers. Presently such types of models have been the subject matter of current research mainly due to its applications in computer and communication systems. One of the most important result deals with such models is "Stochastic Decomposition result", which was first established by Fuhrmann and Cooper [18] for M/G/1 type queues with generalized vacations. Our intention is to look into some sort of unified approach of the results of several models but, to provide simple proof of decompostion results for a single server queue with two phases of service and generalized vacations. Also we will discuss some statistical inference related issues for both two phase queue with out vacations as well as with vacations.

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Section: The Mathematical Modelmentioning

confidence: 99%

A Single Server Queueing System with Two Phases of Service and Vacations

Choudhury

2008

Quality Technology & Quantitative Management

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“…In [ 22 ], the transient results for the number served during a busy period in a

queue was obtained by approximating the interarrival distribution according to a two-phase Cox distribution. A more general model,

, was studied in [ 23 ] using the diffusion approximation technique.…”

Section: Introductionmentioning

confidence: 99%

On the Time to Buffer Overflow in a Queueing Model with a General Independent Input Stream and Power-Saving Mechanism Based on Working Vacations

Kobielnik

Kempa

2021

Sensors

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A single server GI/M/1 queue with a limited buffer and an energy-saving mechanism based on a single working vacation policy is analyzed. The general independent input stream and exponential service times are considered. When the queue is empty after a service completion epoch, the server lowers the service speed for a random amount of time following an exponential distribution. Packets that arrive while the buffer is saturated are rejected. The analysis is focused on the duration of the time period with no packet losses. A system of equations for the transient time to the first buffer overflow cumulative distribution functions conditioned by the initial state and working mode of the service unit is stated using the idea of an embedded Markov chain and the continuous version of the law of total probability. The explicit representation for the Laplace transform of considered characteristics is found using a linear algebra-based approach. The results are illustrated using numerical examples, and the impact of the key parameters of the model is investigated.

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“…Both Zwart [18] and Baltrūnas et al [3] focus on the tail behaviour of the busy periods of GI /G/1-type queues. Ohta and Morii [12] and Agarwal [1] consider finite capacity queues. The former considers the discrete-time M/G/1/N queue whereas the latter considers the GI /M/1 queue.…”

Section: Introductionmentioning

confidence: 99%

An analytic study of a scalable video buffer

et al. 2009

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In this contribution, we investigate the performance of the output buffer of an ‘ondemand’ video streaming server. The server maintains a local database of stored video clips and movies which can be streamed to the users upon request. We assume that the stored video is encoded in a scalable way, which means that the data streams contain a base layer ensuring a minimum of guaranteed quality and a stack of additional enhancement layers progressively improving the quality of the video. For the purpose of performance analysis, we assume that a video stream is split up in logical units called frames. Every frame consists of a number of packets, each containing information of one layer only. When the output buffer gets congested, one may choose to drop the transmission of some of the layers in a frame, thus reducing the frame transmission time and expediting the restoration of the buffer size to normal levels. A discrete-time finite capacity queueing model with buffer size dependent transmission times is proposed. Using a probability generating function approach, we focus on the characteristics of idle and busy periods. We obtain performance measures such as the frame loss ratio and the average frame transmission time. The latter measure relates to the quality of the video stream. We conclude with some numerical examples, including a realistic case study

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Distribution of number served during a busy period of GI/M/1/N queues-lattice path approach

Cited by 10 publications

References 15 publications

A Single Server Queueing System with Two Phases of Service and Vacations

A Single Server Queueing System with Two Phases of Service and Vacations

On the Time to Buffer Overflow in a Queueing Model with a General Independent Input Stream and Power-Saving Mechanism Based on Working Vacations

An analytic study of a scalable video buffer

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