A two-class queueing system with constant retrial policy and general class dependent service times

Dimitriou, Ioannis

doi:10.1016/j.ejor.2018.03.002

Cited by 23 publications

(6 citation statements)

References 47 publications

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“…However, in specific service settings, the intervals between the successive retrials are independent of the number of attempting customers. In such cases, it is assumed that only the customer that is at the "head" of the orbit is allowed to conduct retrials, e.g., [9], or equivalently, the server searches for customers from the orbit after a service completion (i.e., the concept of callback option mentioned above). Such a policy is called the constant retrial policy, and was introduced in a fully Markovian framework in [10].…”

Section: Literature Reviewmentioning

confidence: 99%

The M/G/1 retrial queue with event-dependent arrivals

Dimitriou¹

2022

Preprint

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We introduce a novel single-server queue with general retrial times and event-dependent arrivals. This is a versatile model for the study of service systems, in which the server needs a non-negligible time to retrieve waiting customers upon a service completion, while future arrivals depend on the last realized event. Such a model is motivated by the customers' behaviour in service systems where they decide to join based on the last realized event. We investigate the necessary and sufficient stability condition and derive the stationary distribution both at service completion epochs, and at an arbitrary epoch using the supplementary variable technique. We also study the asymptotic behaviour under high rate of retrials. Performance measures are explicitly derived and extensive numerical examples are performed to investigate the impact of event-dependency. Moreover, constrained optimisation problems are formulated and solved with ultimate goal to investigate the admission control problem.

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Section: Literature Reviewmentioning

confidence: 99%

The M/G/1 retrial queue with event-dependent arrivals

Dimitriou¹

2022

Preprint

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“…Recently, motivated by a contention problem in the downlink direction of wireless base stations in cognitive radio networks, Gao et al [11] presented a repairable M/G/1 retrial queue with the Bernoulli schedule and a general retrial policy. By using the solution of a Riemann boundary value problem, Dimitriou [12] derived the generating function of the stationary distribution of the number of orbiting customers at service completion epochs, and he also gave the explicit expressions for the expected delay in an orbit without solving a boundary value problem. In the study of the continuous-time retrial queueing models, the Markov process is the main mathematical tool.…”

Section: Related Workmentioning

confidence: 99%

Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks

Gao

Wang

2019

Mathematical Problems in Engineering

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is paper presents a discrete-time Geo/G/1 retrial queue with two waiting buffers to model an ATM network, in which the server begins a single vacation in cases where the system is empty at the instant of a service completion. New arriving customer who finds the server being on vacation can decide to either enter the retrial buffer with some probability p or leave the system with complementary probability 1 − p. But the new arriving customer can begin its service immediately if he finds the server idle and join the original buffer if he finds the server busy. We first carry out an extensive analysis of the model by using the supplementary variable method and the generating function approach, and give some performance measures, such as server's state probabilities and mean queue lengths in the original buffer, retrial buffer, and in the system. Secondly, we give the generating function of the sojourn time of a customer in the system and prove that Little's law still holds in our model. Sensitivity analysis and cost optimization are finally given for illustrative purposes.

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“…The aim of this analysis is to offer a review of the work undertaken by researchers in the theory of retrial queueing that is of relevance to scheduling, and to offer a basis for investigating the integration of queueing theory and scheduling methods for resolving problems associated with dynamic scheduling. Recent literature on different types of queuing systems can be found in Chang et al [27] Dimitriou [28].…”

Section: Literature Reviewmentioning

confidence: 99%

Implementation of Fuzzy Logic for M/M/C Model in Packet Switched Network Using HoL Priority Queue

K¹,

Hussain²

2019

IJRAT

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In this paper, an HoL priority queue is utilised to give preference to some high priority traffic using fuzzy logic controller. The same controller is also used to choose the number of servers in M/M/C queue model since this represents the speed of service. The service rate has been altered between one and two for altering the C value in the queue. Using MATLAB, the queuing model is simulated and various performance metrics like utilization factor and mean delay time is obtained for a particular period of time. Also, the number of units have been kept at both high and low and based on that the service rate is altered.

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A two-class queueing system with constant retrial policy and general class dependent service times

Cited by 23 publications

References 47 publications

The M/G/1 retrial queue with event-dependent arrivals

The M/G/1 retrial queue with event-dependent arrivals

Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks

Implementation of Fuzzy Logic for M/M/C Model in Packet Switched Network Using HoL Priority Queue

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