The transient analysis of the queue-length distribution in the batch arrival system with N-policy, multiple vacations and setup times

Kempa, Wojciech M.; Venkov, George; Pasheva, Vesela; Kovacheva, Ralitza

doi:10.1063/1.3515592

Cited by 19 publications

(11 citation statements)

References 8 publications

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“…Representation for a total expected cost per time unit in the stationary state of a M/G/1-type QS with a removable server and a finite buffer was obtained by Teghem (1987). One can find new results for the transient departure process in the M X /G/1 infinite-buffer QS with different-type server vacations e.g., in the works of Kempa (2010c;2011a;, who also gives explicit representations for Laplace transforms of queue-size distribution in models with some mixed vacation policies (Kempa, 2012a). Characteristics of a vacation cycle were investigated also by Kempa (2009;2010a), who additionally analyzed the queueing delay in a finite-buffer queue with single server vacations (Kempa, 2012b).…”

Section: Woźniak Et Almentioning

confidence: 93%

A finite-buffer queue with a single vacation policy: An analytical study with evolutionary positioning

Woźniak

Kempa

Gabryel

et al. 2014

International Journal of Applied Mathematics and Computer Science

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In this paper, application of an evolutionary strategy to positioning a GI/M/1/N -type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical experiments are presented. A cost optimization problem is solved using an evolutionary strategy for a class of queueing systems described by exponential and Erlang distributions.

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Section: Woźniak Et Almentioning

confidence: 93%

A finite-buffer queue with a single vacation policy: An analytical study with evolutionary positioning

Woźniak

Kempa

Gabryel

et al. 2014

International Journal of Applied Mathematics and Computer Science

Self Cite

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“…Compactform formulae for the non-stationary queue-size distribution for some infinite-buffer models were obtained e.g. in [4] and [12].…”

Section: Preliminariesmentioning

confidence: 99%

“…Compactform formulae for the non-stationary queue-size distribution for some infinite-buffer models were obtained e.g. in [4] and [12].The remaining part of the paper is organized as follows. In the next Section 2 the system of integral equations for the time-dependent queue-size distributions, conditioned by the number of packets at t = 0, is obtained, using the approach based on the idea of embedded Markov chain and the law of total probability.…”

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confidence: 99%

Time-Dependent Queue-Size Distribution in the Finite GI/M/l Model with AQM-Type Dropping

Kempa¹

2013

AEI

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A GI/M/1-type queueing system with finite buffer capacity and AQM-type packet dropping is investigated. Even when the buffer is not saturated an incoming packet can be dropped (lost) with probability dependent on the instanteneous queue size. The system of integral equations for time-dependent queue-size distribution conditioned by the number of packets present in the system initially is built using the embedded Markov chain approach. The solution of the corresponding system written for Laplace transforms is found using the linear algebra. Numerical examples, in which different-type dropping functions are investigated in some network-motivated traffic scenarios, are attached as well.Keywords: AQM (Active Queue Management), dropping function, finite buffer, queue size, time-dependent distribution. PRELIMINARIESThe phenomenon of packet losses is a typical one in packet-oriented networks like e.g. the Internet. Obviously, due to finite capacities of IP routers' buffers, the queue of packets waiting for processing can not be unbounded. In consequence, during the buffer overflow period all the incoming packets are naturally lost (Tail Drop algorithm). Unfortunately, such a policy has different disadvantages. For example, it is difficult to stabilize the arrival intensity on the proper level and hence many retransmissions are necessary. The Active Queue Management (AQM), in the contrast to Passive Queue Management (PQM), based on the idea of Tail Drop, allows for dropping the arriving packets even when the buffer is not completely saturated. The dropping probability can depend on the mean or instanteneous queue size. In consequence the reduction of the buffer queue length is being obtained in two diffrent ways:• by immediate deleting the incoming packet via dropping function (short-term reduction);• by decreasing the intensity of arrivals as a reaction of the source host for packet dropping, according to TCP/IP protocol requirements (long-term reduction).In [8] the first model with AQM-type packet dropping was introduced, with a linear dropping function. Looking for the mathematical description of the packet dropping function being optimal with respect to one or more criteria, resulted in many papers in which some other shapes of dropping functions were proposed and investigated. In this article an algebraic method for computing timedependent queue-size distribution in the finite-buffer model with general-type independent input stream and packet dropping is proposed. There are at least two main motivations for such a study. The first one is that in the literature the results concerning models with AQM are obtained mainly for the equilibrium. The next is that they are often restricted to the case of Poisson (or compound Poisson) arrival process.Transient results for the finite GI/M/1-type queueing models can be found e.g. in [10], [11] and [14]. Compactform formulae for the non-stationary queue-size distribution for some infinite-buffer models were obtained e.g. in [4] and [12].The remaining part of the paper i...

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“…Transient results for queue-size distribution is some other queueing models can be found e.g. in [4], [5], [6], [7] and [8].…”

Section: Introductionmentioning

confidence: 99%

The transient analysis of the queue-length distribution in the batch arrival system with N-policy, multiple vacations and setup times

Cited by 19 publications

References 8 publications

A finite-buffer queue with a single vacation policy: An analytical study with evolutionary positioning

A finite-buffer queue with a single vacation policy: An analytical study with evolutionary positioning

Time-Dependent Queue-Size Distribution in the Finite GI/M/l Model with AQM-Type Dropping

Transient queue-size distribution in a finite-capacity queueing system with server breakdowns and Bernoulli feedback

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