Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues

Chaudhry, M. L.; Kim, James J.; Banik, Abhijit Datta

doi:10.1155/2019/6480139

Cited by 5 publications

(3 citation statements)

References 31 publications

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“…One possible extension of this work is to examine the case of infinite capacity waiting stations for all classes of priority. This can be approached through the method of roots as discussed in papers by Chaudhry et al [42]. It is also interesting to compare two different situations: in one, the external customers join only in the highest priority line, and in the second, low priority customers join in the respective queues.…”

Section: Discussionmentioning

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: Discussionmentioning

confidence: 99%

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

Nair¹,

Krishnamoorthy

Melikov

et al. 2021

Mathematics

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“…Te direct nontransform approach in Teorem 30 is similar to the approach used by Chaudhry et al [37] to compute the waiting time distribution in a batch arrival multiserver system. Tis approach is later utilized in Chaudhry et al [38].…”

Section: Waiting Time Distribution Functionmentioning

confidence: 99%

A Review of Birth-Death and Other Markovian Discrete-Time Queues

El-Taha

2023

Advances in Operations Research

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In this review article, we consider discrete-time birth-death processes and their applications to discrete-time queues. To make the analysis simpler to follow, we focus on transform-free methods and consider instances of non-birth-death Markovian discrete-time systems. We present a number of results within one discrete-time framework that parallels the treatment of continuous time models. This approach has two advantages; first, it unifies the treatment of several discrete-time models in one framework, and second, it parallels to the extent possible the treatment of continuous time models. This allows us to draw parallels and contrasts between the discrete and continuous time queues. Specifically, we focus on birth-death applications to the single server discrete-time model with Bernoulli arrivals and geometric service times and provide the reader with a simple rigorous detailed analysis that covers all five scheduling rules considered in the literature, with attention to stationary distributions at slot edges, slot centers, and prearrival epochs. We also cover the waiting time distributions. Moreover, we cover three Markovian models that fit the global balance equations. Our approach provides interesting insights into the behavior of discrete-time queues. The article is intended for those who are familiar with queueing theory basics and would like a simple, yet rigorous introductory treatment to discrete-time queues.

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“…Most papers, however, focus on the analysis of the queue length characteristics only. Results are available for queueing systems with a constant number of available servers [4][5][6] as well as for queueing systems with a variable number of available servers [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals

2021

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In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characterized by its own distributions for the number of arrivals and the number of available servers in a slot. Within a state, these numbers are independent and identically distributed random variables. State changes can only occur at slot boundaries and mark the beginnings and ends of state periods. Each state has its own distribution for its period lengths, expressed in the number of slots. The stochastic process that describes the state changes introduces correlation to the system, e.g., long periods with low arrival intensity can be alternated by short periods with high arrival intensity. Using probability generating functions and the theory of the dominant singularity, we find the tail probabilities of the delay.

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Analytically Simple and Computationally Efficient Results for the GI^X/Geo/c Queues

Cited by 5 publications

References 31 publications

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

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

A Review of Birth-Death and Other Markovian Discrete-Time Queues

Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals

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