Queue-Size Distribution in M/G/1-Type System with Bounded Capacity and Packet Dropping

Tikhonenko, Oleg; Kempa, Wojciech M.

doi:10.1007/978-3-642-35980-4_20

Cited by 25 publications

(19 citation statements)

References 8 publications

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“…In the work of Tikhonenko and Kempa (2012), the formula for the queue-size distribution was obtained for a stationary M/M/1/N -type system with the above-mentioned generalized arrival process, in which the incoming packets have generally distributed volumes and the total system capacity is bounded. An extension of results obtained by Tikhonenko and Kempa (2012) for the case of a multi-channel model is included in their further work (Tikhonenko and Kempa, 2013). New results for time-dependent queue-size distributions in finite AQM-type models were obtained by Kempa (2013a;2013b;2013c).…”

Section: Introductionmentioning

confidence: 95%

“…In this model the notion of a "finite buffer" stands for a certain nonrandom maximal buffer capacity V, not for the maximal number of packets being allowed for waiting for service in the waiting room (Tikhonenko, 1991;2005;Tikhonenko and Kempa, 2012;2013;2015). It seems such a model can be better adjusted to real-life packet-oriented networks modeling, in which the volume of the buffer measured in bytes (not in packets) is deterministic.…”

Section: Introductionmentioning

confidence: 99%

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Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping

Tikhonenko

Kempa

2016

International Journal of Applied Mathematics and Computer Science

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A queueing system of the M/G/n-type, n ≥ 1, with a bounded total volume is considered. It is assumed that the volumes of the arriving packets are generally distributed random variables. Moreover, the AQM-type mechanism is used to control the actual buffer state: each of the arriving packets is dropped with a probability depending on its volume and the occupied volume of the system at the pre-arrival epoch. The explicit formulae for the stationary queue-size distribution and the loss probability are found. Numerical examples illustrating theoretical formulae are given as well.

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping

Tikhonenko

Kempa

2016

International Journal of Applied Mathematics and Computer Science

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“…The random dropping of arrivals is a powerful tool for parameter control of a queueing system. Each arriving customer can be accepted for service with a probability depending on the queue length at the time of arrival of the customer, even if the buffer is not completely full [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…Using equations (1), we have the equalities (4) and from the equations (16) we obtain the recurrence relations: …”

mentioning

confidence: 99%

Steady-state characteristics of three-channel queueing systems with Erlangian service times

Kopytko

Zhernovyi

2016

J. Appl. Math. Comput. Mech.

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Abstract. We propose a method of study the M/E 2 /3/∞ queueing systems: standard system and systems with the threshold and hysteretic strategies of the random dropping of customers in order to control the input flow. Recurrence relations to compute the stationary distribution of the number of customers and the steady-state characteristics are obtained. The developed algorithms are tested on examples using simulation models constructed with the assistance of the GPSS World tools.

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“…The use of the queuing theory to analyze the active queue management algorithms started in recent years [1,[4][5][6][7][8]. As a rule, the authors restrict the study of systems with exponential distribution of the service time and in the case of consideration of the general law of the service time distribution, the assumption of ordinary input flow is used.…”

Section: Introductionmentioning

confidence: 99%

On characteristics of the M^theta/G/1/m and M^theta/G/1 queues with queue-size based packet dropping

Zhernovyi¹,

Kopytko²,

Zhernovyi³

2014

J. Appl. Math. Comput. Mech.

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Abstract. We study the M θ /G/1/m and M θ /G/1 queuing systems with the function of the random dropping of customers used to ensure the required characteristics of the system. Each arriving packet of customers can be rejected with a probability defined depending on the queue length at the service beginning of each customer. The Laplace transform for the distribution of the number of customers in the system on the busy period is found, the mean duration of the busy period is determined, and formulas for the stationary distribution of the number of customers in the system are derived via the approach based on the idea of Korolyuk's potential method. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.Keywords: queuing systems, packet arrival of customers, active queue management, random dropping of customers, busy period, distribution of the number of customers

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Queue-Size Distribution in M/G/1-Type System with Bounded Capacity and Packet Dropping

Cited by 25 publications

References 8 publications

Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping

Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping

Steady-state characteristics of three-channel queueing systems with Erlangian service times

On characteristics of the M^theta/G/1/m and M^theta/G/1 queues with queue-size based packet dropping

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Queue-Size Distribution in M/G/1-Type System with Bounded Capacity and Packet Dropping

Cited by 25 publications

References 8 publications

Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping

Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping

Steady-state characteristics of three-channel queueing systems with Erlangian service times

On characteristics of the Mtheta/G/1/m and Mtheta/G/1 queues with queue-size based packet dropping

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On characteristics of the M^theta/G/1/m and M^theta/G/1 queues with queue-size based packet dropping