Methods for Computing a System with Instantaneous Feedback and Variable Input Stream Intensity

Melikov, Agassi; Aliyeva, Sevinj; Shahmaliyev, Mammed O.

doi:10.1134/s0005117920090052

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…Melikov et al [18] discuss methods to calculate the system state distribution with instantaneous feedback and a varying arrival rates in a Markov model of a servicing system with one server. At a service completion epoch, the customer either leaves the system or immediately returns to receive the service, which is repeated according to a predefined Bernoulli scheme.…”

Section: Literature Review Of Feedback Queuesmentioning

confidence: 99%

MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback

Nair¹,

Krishnamoorthy

Melikov

et al. 2021

Mathematics

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In this paper, we consider two single server queueing systems to which customers of two distinct priorities (P1 and P2) arrive according to a Marked Markovian arrival process (MMAP). They are served according to two distinct phase type distributions. The probability of a P1 customer to feedback is θ on completion of his service. The feedback (P1) customers, as well as P2 customers, join the low priority queue. Low priority (P2) customers are taken for service from the head of the line whenever the P1 queue is found to be empty at the service completion epoch. We assume a finite waiting space for P1 customers and infinite waiting space for P2 customers. Two models are discussed in this paper. In model I, we assume that the service of P2 customers is according to a non-preemptive service discipline and in model II, the P2 customers service follow a preemptive policy. No feedback is permitted to customers in the P2 line. In the steady state these two models are compared through numerical experiments which reveal their respective performance characteristics.

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Section: Literature Review Of Feedback Queuesmentioning

confidence: 99%

MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback

Nair¹,

Krishnamoorthy

Melikov

et al. 2021

Mathematics

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“…Over the past few years, queueing models with Bernoulli feedback have increasingly attracted the attention of many researchers [9]- [14]. Taking into account the feedback effect makes it possible to bring the considered models closer to a real situation, where the claims once serviced may require repeat service for different reasons.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

Bouchentouf

Medjahri

Boualem

et al. 2022

Discrete and Continuous Models

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In this paper, we analyze a multi-server queue with customers impatience and Bernoulli feedback under a variant of multiple vacations. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size as well as the status of the servers. It is supposed that customer impatience can arise both during busy and vacation period because of the long wait already experienced in the system. The latter can be retained via certain mechanism used by the system. The feedback occurs as returning a part of serviced customers to get a new service. The queue under consideration can be used to model the processes of information transmission in telecommunication networks. We develop the Chapman-Kolmogorov equations for the steady-state probabilities and solve the differential equations by using the probability generating function method. In addition, we obtain explicit expressions of some important system characteristics. Different queueing indices are derived such as the probabilities when the servers are in different states, the mean number of customers served per unit of time, and the average rates of balking and reneging.

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Methods for Computing a System with Instantaneous Feedback and Variable Input Stream Intensity

Cited by 2 publications

References 13 publications

MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback

MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback

Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

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