Stochastic Decomposition in M/M/  Queues with Markov Modulated Service Rates

Baykal‐Gürsoy, Melike; Xiao, Weihua

doi:10.1023/b:ques.0000039888.52119.1d

Cited by 71 publications

(74 citation statements)

References 19 publications

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“…The first one is the number of customers at equilibrium in an ordinary M/M/∞ system with no interruptions, while the second one is a positive random variable that depends on all the parameters of the system. This extends the results of [2] for the case μ = 0 and for this case we also give a different decomposition of the second term. Before stating the theorem, let the functionL(·) be the LST of the functionL(·) that we define as the residual life time of the OFF period, i.e., 1 rL (y)dy}, while X has characteristic functionL(λ (1 − z)).…”

Section: Stochastic Decompositionsupporting

confidence: 60%

“…Firstly we want to investigate the possibility to express the number of customers in the system with interruptions by the sum of two independent terms, the first one being the random variable associated to the system with no interruptions and the second one being a positive random variable. In this sense we extend some of the results of Baykal-Gursoy and Xiao [2] that looked at an M/M/∞ system with Markov-modulated service rate. They were able to get explicit formulas assuming that the OFF periods were exponentially distributed as well.…”

Section: Introduction and Model Descriptionmentioning

confidence: 89%

“…In the result of [2] and [11], where all the involved distributions are exponential or a mixture of exponentials, it turned out that the number of customers in the systems was not Poisson distributed but still its distribution had an exponential tail decay. In our case we relax the exponential assumption and we look at regularly varying distributions.…”

Section: Introduction and Model Descriptionmentioning

confidence: 99%

See 2 more Smart Citations

M/M/∞ Queue with ON-OFF Service Speeds

D’Auria¹

2013

J Math Sci

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In this paper we analyze of a special kind of M/M/∞ queueing system. We assume that the rate of the servers alternates between two speeds according to an ON-OFF process whose ON periods are exponentially distributed and with general OFF periods. We look at the particular case where the OFF service rate is zero while the distribution of the OFF periods is heavy tailed, and for this case we derive the tail of the number of customers in the system. This model be applied to transportation systems where the M/M/∞ represents a delay line, such as a highway, whose crossing time may be unexpectedly interrupted for a long time by some accident.

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Section: Stochastic Decompositionsupporting

confidence: 60%

Section: Introduction and Model Descriptionmentioning

confidence: 89%

Section: Introduction and Model Descriptionmentioning

confidence: 99%

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M/M/∞ Queue with ON-OFF Service Speeds

D’Auria¹

2013

J Math Sci

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“…Baykal-Gursoy and Xiao [4] consider a steady-state m/m/∞ queuing system subjected to random interruptions of exponentially distributed durations. Total system breakdown and partial failure were investigated, and in both cases present the expected number of vehicles in the system.…”

Section: Literature Reviewmentioning

confidence: 99%

Traffic flow model at fixed control signals with discrete service time distribution

Igbinosun¹,

Omosigho²

2016

Croat. Oper. Res. Rev.

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Abstract.Most of the models of road traffic flow at fixed-cycle controlled intersection assume stationary distributions and provide steady state results. The assumption that a constant number of vehicles can leave the system during the green phase is unrealistic in real life situations. A discrete time queuing model was developed to describe the operation of traffic flow at a road intersection with fixed-cycle signalized control and to account for the randomness in the number of vehicles that can leave the system. The results show the expected queue size in the system when the traffic is light and for a busy period, respectively. For the light period, when the traffic intensity is less than one, it takes a shorter green cycle time for vehicles to clear up than during high traffic intensity (the road junction is saturated). Increasing the number of cars that can leave the junction at the turn of the green phase reduces the number of cycle times before the queue is cleared.

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“…We leverage the results on queues with interruptions [4]. The work [5] models the EV demand systems as M/M/n queues, but does not consider the dynamically disconnecting scenarios as in smart grids.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Electric Vehicle Charging Systems in Communications Enabled Smart Grids

Baek

Kim²,

Oh³

et al. 2011

IEICE Trans. Inf. & Syst.

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SUMMARYWe consider a queuing model with applications to electric vehicle (EV) charging systems in smart grids. We adopt a scheme where an Electric Service Company (ESCo) broadcasts a one bit signal to EVs, possibly indicating 'on-peak' periods during which electricity cost is high. EVs randomly suspend/resume charging based on the signal. To model the dynamics of EVs we propose an M/M/∞ queue with random interruptions, and analyze the dynamics using time-scale decomposition. There exists a trade-off: one may postpone charging activity to 'off-peak' periods during which electricity cost is cheaper, however this incurs extra delay in completion of charging. Using our model we characterize achievable trade-offs between the mean cost and delay perceived by users. Next we consider a scenario where EVs respond to the signal based on the individual loads. Simulation results show that peak electricity demand can be reduced if EVs carrying higher loads are less sensitive to the signal. key words: queuing systems, time-scale decomposition, quality of service, plug-in hybrid electric vehicles

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Stochastic Decomposition in M/M/ Queues with Markov Modulated Service Rates

Cited by 71 publications

References 19 publications

M/M/∞ Queue with ON-OFF Service Speeds

M/M/∞ Queue with ON-OFF Service Speeds

Traffic flow model at fixed control signals with discrete service time distribution

Modeling of Electric Vehicle Charging Systems in Communications Enabled Smart Grids

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