scispace - formally typeset
Search or ask a question
Journal ArticleDOI

State dependent arrival in bulk retrial queueing system with immediate Bernoulli feedback, multiple vacations and threshold

01 Nov 2017-Vol. 263, Iss: 4, pp 042144
About: The article was published on 2017-11-01 and is currently open access. It has received 4 citations till now. The article focuses on the topics: Bernoulli's principle.
Citations
More filters
Journal ArticleDOI
TL;DR: This paper analyzes a discrete-time batch-service queue with two customer classes and deduces the system occupancy and its approximations at random slot boundaries, and proposes a method for interpolating between these approximation in order to study the behaviour in the intermediate region.
Abstract: In multi-class telecommunications or manufacturing systems, customers belonging to the same class can often be processed together. This results in a service capacity that depends on the classes of the customers in the queue. In this paper, we analyse a discrete-time batch-service queue with two customer classes. The single batch server can group all same-class customers at the head of the queue up to a constant class-dependent maximum service capacity. We focus on the analysis of the system occupancy at service initiation opportunities, and also compute both a light- and heavy traffic approximation in order to reduce the numerical complexity introduced by the maximum service capacities. Additionally, we propose a method for interpolating between these approximations in order to study the behaviour in the intermediate region. We also deduce the system occupancy and its approximations at random slot boundaries. In the numerical experiments, we examine the conditions under which these proposed approximations are accurate.

2 citations


Cites background from "State dependent arrival in bulk ret..."

  • ...Batch-service queueing systems are often found in manufacturing (Niranjan et al. 2017), transportation systems (Bountali and Economou 2017), and telecommunication systems (Bellalta and Oliver 2009) where packets are grouped together based on similarities in the production process or destination....

    [...]

DOI
04 Jul 2021
TL;DR: The concept of differentiated vacations in a retrial queueing model with state dependent arrival rates of customers is introduced and the system size probabilities and other system performance measures are obtained.
Abstract: In present paper we have introduced the concept of differentiated vacations in a retrial queueing model with state dependent arrival rates of customers. The arrival rate of customers is different in various states of the server. The vacation types are differentiated by means of their durations as well as the previous state of the server. In type I vacation, server goes just after providing service to at least one customer whereas in type II, it comes after remaining free for some time. In steady state, we have obtained the system size probabilities and other system performance measures. Finally, sensitivity and cost analysis of the proposed model is also performed. The probability generating function technique, parabolic method and MATLAB is used for the purpose.

1 citations


Cites background from "State dependent arrival in bulk ret..."

  • ...[12] did the pioneer work on state dependent arrival in bulk retrial queues with Bernoulli feedback and multiple vacations....

    [...]

Book ChapterDOI
01 Jan 2022
TL;DR: In this article , a general service batch arrival feedback retrial G-queue with vacation is considered, where the server provides service in S phases and there are several different optional services available at each level.
Abstract: General service batch arrival feedback retrial G-queue with vacation is considered. Along with the essential service, the server provides service in S phases. There are several different optional services available at each level. The server’s status determines whether or not each individual customer is admitted to the system. According to the Poisson process, positive customers arrive in batches. When a negative consumer enters the system, the server goes down and the customer in service is removed from the system. The failing server is immediately dispatched for repair. If the server is idle, one of the admitted customer instantly enters the service and the others join the orbit; otherwise, all admitted customers enter the orbit. After the completion of essential or optional services, the server may join the queue if they are dissatisfied with the service. The server will leave on vacation with certain probability, after providing service to a customer. The system’s probability generating functions are carried out using the supplemental variable approach, and various performance measurements are developed. Stochastic decomposition property is verified and the special cases are deduced. The joint distributions of the server state and the number of customers in the retrial group are obtained. The influence of parameters on system performance metrics is investigated.
References
More filters
Journal ArticleDOI
TL;DR: Various characteristics of the queueing system and a cost model with the numerical solution for a particular case of the model are presented.

92 citations

Journal ArticleDOI
TL;DR: A recursive scheme to compute the distribution of the number of served customers during the k-busy period and the ordinary busy period of the M[X]/G/1 retrial queue and the effects of several parameters on the system are analysed numerically.
Abstract: We consider an M[X]/G/1 retrial queue subject to breakdowns where the retrial time is exponential and independent of the number of customers applying for service. If a coming batch of customers finds the server idle, one of the arriving customers begins his service immediately and the rest joins a retrial group (called orbit) to repeat his request later; otherwise, if the server is busy or down, all customers of the coming batch enter the orbit. It is assumed that the server has a constant failure rate and arbitrary repair time distribution. We study the ergodicity of the embedded Markov chain, its stationary distribution and the joint distribution of the server state and the orbit size in steady-state. The orbit and system size distributions are obtained as well as some performance measures of the system. The stochastic decomposition property and the asymptotic behavior under high rate of retrials are discussed. We also analyse some reliability problems, the k-busy period and the ordinary busy period of our retrial queue. Besides, we give a recursive scheme to compute the distribution of the number of served customers during the k-busy period and the ordinary busy period. The effects of several parameters on the system are analysed numerically.

44 citations

Journal ArticleDOI
TL;DR: A batch arrival retrial queue with general retrial times under a modified vacation policy with potential applications in packet-switched networks is considered and some important system characteristics are derived.

41 citations

Journal ArticleDOI
TL;DR: This paper deals with the steady-state behavior of an M^X/G/1 retrial queue with an additional second phase of optional service and service interruption where breakdowns occur randomly at any instant while the server is serving the customers.
Abstract: This paper deals with the steady-state behavior of an M^X/G/1 retrial queue with an additional second phase of optional service and service interruption where breakdowns occur randomly at any instant while the server is serving the customers. Further, the concept of delay time is also introduced in the model. This model generalizes both the classical M^X/G/1 retrial queue with service interruption as well as the M^X/G/1 queue with second optional service and service interruption. We carry out an extensive analysis of this model.

40 citations