Sojourn times in single-server queues by negative customers

Harrison, Peter G.; Pitel, Edwige

doi:10.2307/3214524

Cited by 77 publications

(15 citation statements)

References 9 publications

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“…Finally, (25) is true because 0 and 1 are absorbing states. This last fact can also be deduced from (24).…”

Section: Theoremmentioning

confidence: 76%

“…Also, substituting (29) and (30) into (28) yields (24). Finally, (25) is true because 0 and 1 are absorbing states.…”

Section: Theoremmentioning

confidence: 88%

“…Expression (24) can also be used to obtain information about the expectation of the process. Let m * i (t) = E i (X * (t)) and denote its Laplace transform by…”

Section: Theoremmentioning

confidence: 99%

“…Now, (24) and (25), where Υ k (λ, s) = ∞ j =0 φ * kj (λ)s j . Using (24), the first term in J 1 can be further written as…”

Section: Construction Theorem and Recurrence And Equilibrium Propertiesmentioning

confidence: 99%

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Markovian bulk-arrival and bulk-service queues with state-dependent control

Chen

Pollett

et al. 2010

Queueing Syst

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We study a modified Markovian bulk-arrival and bulk-service queue incorporating state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated and the relationship with our queueing model is examined and exploited. Equilibrium behaviour is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting time and busy period distributions are answered in detail and the Laplace transforms of these distributions are presented. Further properties including expectations of hitting times and busy period are also explored. A. Chen ( )

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“…Finally, (25) is true because 0 and 1 are absorbing states. This last fact can also be deduced from (24).…”

Section: Theoremmentioning

confidence: 76%

“…Also, substituting (29) and (30) into (28) yields (24). Finally, (25) is true because 0 and 1 are absorbing states.…”

Section: Theoremmentioning

confidence: 88%

“…Expression (24) can also be used to obtain information about the expectation of the process. Let m * i (t) = E i (X * (t)) and denote its Laplace transform by…”

Section: Theoremmentioning

confidence: 99%

“…Now, (24) and (25), where Υ k (λ, s) = ∞ j =0 φ * kj (λ)s j . Using (24), the first term in J 1 can be further written as…”

Section: Construction Theorem and Recurrence And Equilibrium Propertiesmentioning

confidence: 99%

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Markovian bulk-arrival and bulk-service queues with state-dependent control

Chen

Pollett

et al. 2010

Queueing Syst

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“…We consider here two variants of the RCE killing discipline (removal of the customer from the end of the queue), where the most recent positive arrivals are removed [16] first. The first variant, RCE-inimmune servicing, removes the most recent positive arrival regardless of whether it is in service or waiting; a negative arrival has no effect only when it encounters an empty queue and all servers idle.…”

Section: Negative Customersmentioning

confidence: 99%

A Markov modulated multi-server queue with negative customers – The MM CPP/GE/c/L G-queue

Chakka¹,

Harrison²

2001

Acta Informatica

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We obtain the queue length probability distribution at equilibrium for a multi-server queue with generalised exponential service time distribution and either finite or infinite waiting room. This system is modulated by a continuous time Markov phase process. In each phase, the arrivals are a superposition of a positive and a negative arrival stream, each of which is a compound Poisson process with phase dependent parameters, i.e. a Poisson point process with bulk arrivals having geometrically distributed batch size. Such a queueing system is well suited to B-ISDN/ATM networks since it can account for both burstiness and correlation in traffic. The result is exact and is derived using the method of spectral expansion applied to the two dimensional (queue length by phase) Markov process that describes the dynamics of the system. Several variants of the system are considered, applicable to different modelling situations, such as server breakdowns, cell losses and load balancing.We also consider the departure process and derive its batch size distribution and the Laplace transform of the interdeparture time probability density function. From this, a recurrence formula is obtained for its moments. The analysis therefore provides the basis of a building block for modelling networks of switching nodes in terms of their internal arrival processes.

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The MM CPP/GE/c/L G-Queue at equilibrium

Harrison

Chakka

2001

Performance and QoS of Next Generation Networking

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Sojourn times in single-server queues by negative customers

Cited by 77 publications

References 9 publications

Markovian bulk-arrival and bulk-service queues with state-dependent control

Markovian bulk-arrival and bulk-service queues with state-dependent control

A Markov modulated multi-server queue with negative customers – The MM CPP/GE/c/L G-queue

The MM CPP/GE/c/L G-Queue at equilibrium

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