Stochastic decompositions in the M/M/1 queue with working vacations

Liu, Wenyuan; Xu, Xiuli; Tian, Naishuo

doi:10.1016/j.orl.2006.12.007

Cited by 129 publications

(43 citation statements)

References 10 publications

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“…Banik, Gupta and Pathak [10] analyzed the GI/ M/1/N queue with working vacations. Liu, Xu and Tian [11] established a stochastic decomposition result in the M/M/1 queue with working vacations. In [12], Krishnamoorthy and Sreenivasan considered an M/M/2 queueing system with heterogeneous servers where one server is always available and the other goes on a working vacation when there are no customers in the system.…”

Section: Introductionmentioning

confidence: 99%

M/G/1 Vacation Queueing Systems with Server Timeout

Ibe¹

2015

AJOR

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We consider a single-server vacation queueing system that operates in the following manner. When the server returns from a vacation, it observes the following rule. If there is at least one customer in the system, the server commences service and serves exhaustively before taking another vacation. If the server finds the system empty, it waits a fixed time c. At the expiration of this time, the server commences another vacation if no customer has arrived; otherwise, it serves exhaustively before commencing another vacation. Analytical results are derived for the mean waiting time in the system. The timeout scheme is shown to be a generalized scheme of which both the single vacation and multiple vacations schemes are special cases, with = ∞ c and = 0 c , respectively. The model is extended to the N-policy vacation queueing system.

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Section: Introductionmentioning

confidence: 99%

M/G/1 Vacation Queueing Systems with Server Timeout

Ibe¹

2015

AJOR

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“…This policy is introduced by Servi and Finn [4] and known as multiple working vacations (MWV). The stochastic decomposition forms of the waiting time and queue length in an / /1/WV queue have been established in Liu et al [5]. Intending to use the server efficiently, vacation interruption has become a significant aspect.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Impatient Customers in Queues with Bernoulli Schedule Working Vacations and Vacation Interruption

Goswami

2014

Journal of Stochastics

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This paper analyzes customers' impatience in Markovian queueing system with multiple working vacations and Bernoulli schedule vacation interruption, where customers' impatience is due to the servers' vacation. During the working vacation period, if there are customers in the queue, the vacation can be interrupted at a service completion instant and the server begins a regular busy period with probability 1 − or continues the vacation with probability . We obtain the probability generating functions of the stationary state probabilities and deduce the explicit expressions of the system sizes when the server is in a normal service period and in a Bernoulli schedule vacation interruption, respectively. Various performance measures such as the mean system size, the proportion of customers served, the rate of abandonment due to impatience, and the mean sojourn time of a customer served are derived. We obtain the stochastic decomposition structures of the queue length and waiting time. Finally, some numerical results to show the impact of model parameters on performance measures of the system are presented.

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“…Vacation queues and retrial queues have been applied to evaluate the performance of various systems [1,2,3,4,5,6,7,8,9,10]. Recently, the M/M/1 retrial queue with working vacations was introduced [11] and analyzed.…”

Section: Introductionmentioning

confidence: 99%

M/M/1 retrial queue with working vacations and negative customer arrivals

Papp

Chakka

et al. 2014

IJAIP

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Abstract:The M/M/1 retrial queue with working vacations and negative customers is introduced. The arrival processes of positive customers and negative customers are Poisson. Upon the arrival of a positive customer, if the server is busy the customer would enter an orbit of infinite size and the orbital customers send their requests for service with a constant retrial rate. The single server takes an exponential working vacation once customers being served depart from the system and no customers are in the orbit. Arriving negative customers kill a batch of the positive customers waiting in the orbit randomly. Efficient methodology to compute the stationary distribution for this new queue is developed and presented. Keywords: retrial queue, working vacations, negative customersReference to this paper should be made as follows: Do, T.V, Papp, D., Chakka, R., Sztrik, J. He has participated and lead work packages in the COPERNICUS-ATMIN 1463, the FP4 ACTS AC310 ELISA, FP5 HELINET, FP6 CAPANINA projects funded by EC (where he acted as a work package leader). He led various projects on network planning and software implementations that results are directly used for industry such ATM & IP network planning software for Hungarian Telekom, GGSN tester for Nokia, performance testing program for the performance testing of the NOKIAs IMS product, automatic software testing framework for Nokia Siemens Networks. His research interests are queuing theory, telecommunication networks, cloud computing, performance evaluation and planning of ICT Systems.Denes Papp is a researcher in the Analysis, Design and Development of ICT systems (AddICT) Laboratory. He has participated in various software projects with NOKIA and Nokia Siemens Networks.

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Stochastic decompositions in the M/M/1 queue with working vacations

Cited by 129 publications

References 10 publications

M/G/1 Vacation Queueing Systems with Server Timeout

M/G/1 Vacation Queueing Systems with Server Timeout

Analysis of Impatient Customers in Queues with Bernoulli Schedule Working Vacations and Vacation Interruption

M/M/1 retrial queue with working vacations and negative customer arrivals

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