Bulk Service Queueing System Research Articles

Performance analysis of a versatile bulk-service queue with group-arrival, batch-size-dependent service time and queue-length-dependent vacation

ABSTRACT Queueing systems with bulk-service and vacation policy have become one of the pivotal interest for the researchers due to their widespread application in food processing technology, manufacturing systems, power consumption in small cell base stations etc. This article analyzes a single server versatile bulk-service queueing system wherein the customers arrive according to a compound Poisson process and the service time is dependent on the batch size of undergoing service. Moreover, single and multiple vacation policies have been incorporated along with queue-length-dependent vacation. After providing the steady-state system equations, the bivariate probability generating function of queue and server content distribution together has been derived at departure epoch. After the evaluation of the unknown probabilities, complete joint distributions have been extracted in terms of roots of the denominator of the bivariate probability generating function. The discussed procedure and the reported results have been depicted through some numerical examples for different service and vacation time distributions. Some significant observation about the model has been sketched graphically.

Analysis of Flexible Batch Service Queueing System to Constrict Waiting Time of Customers

When the required number of customers is available in the general bulk service (GBS) queueing system, the server begins service. Otherwise, the server will remain inactive until the number of consumers in the queue reaches that minimum required number. Customers that have already come must wait throughout this time, regardless of their arrival time. In some circumstances, like specimens awaiting testing in a clinical laboratory or perishable commodities awaiting delivery, it is necessary to finish services before the expiration date. It might only be achievable if consumers’ waiting times are kept under control. As a result, the flexible general bulk service (FGBS) rule is developed in this article to provide flexibility in batching. The effectiveness of FGBS implementation has been demonstrated using two examples: a clinical laboratory and a distribution center. To justify the suggested model, a simulation study and numerical illustration are provided.

Analysis of customer's impatience on bulk service queueing system with unreliable server, setup time and two types of multiple vacations

In this investigation, we analyse the customer's impatience on unreliable bulk queueing system with two types of vacation. Depending upon the length of queue, the server is permitted to take two types of vacation called type I vacation and type II vacation. The server is possibly affected by breakdowns and takes considerable time for setup before the repair begins to start. After repair completion, the server will start its remaining service to the batch of customers whose service was interrupted. It could be assumed that the arriving units may be balked from the system when the server is on vacation (type I or type II). By incorporating the supplementary variables technique, the probability generating function of the queue size at an arbitrary and departure time epoch for the designed queueing system are derived. Finally, the stability condition, some performance measures, particular cases are obtained with appropriate numerical illustrations and graphical presentation.

Queue-Length, Waiting-Time and Service Batch Size Analysis for the Discrete-Time GI/D-MSP$^{\text {(a,b)}}/1/\infty $ Queueing System

This paper analyzes an infinite-buffer single-server bulk-service queueing system in which customers arrive according to a discrete-time renewal process. The customers are served under the discrete-time Markovian service process according to the general bulk-service rule. The matrix-geometric method is used to obtain the queue-length distribution at prearrival epoch. The queue-length distributions at other various time epochs are also derived based on prearrival epoch probabilities. A simple approach has been developed to compute the waiting-time distribution of an arriving customer. We also carried out closed-form analytical expression for the service batch size distribution of an arriving customer. Some numerical results are provided in the form of tables for a variety of interarrival-time distributions and model parameters to understand the system behaviour.

Computational approach for transient behaviour of M/M (a, b)/1 bulk service queueing system with working vacation

A new computational technique is used to evaluate the Transient behaviour of Single Server Bulk Service Queueing System with Working Vacation with arrival rate λ which follows a Poisson process and the service will be in bulk. In this model the server provides two types of services namely normal service and lower service. The normal service time follows an exponential distribution with parameter μ 1 . The lower service rate follows an exponential distribution with parameter μ 2 . The vacation time follows an exponential distribution with parameter α. According to Neuts, the server begins service only when a minimum of ‘a’ customers in the waiting room and a maximum service capacity is ‘b’. An infinitesimal generator matrix is formed for all transitions. Time dependent solutions and Steady state solutions are acquired by using Cayley Hamilton theorem. Numerical studies have been done for Time dependent average number of customers in the queue, Transient probabilities of server in vacation and server busy for several values of t, λ, µ 1 , μ 2 , α, a and b.

Resource Allocation in One-dimensional Distributed Service Networks with Applications

We consider assignment policies that allocate resources to users, where both resources and users are located on a one-dimensional line [0,∞). First, we consider unidirectional assignment policies that allocate resources only to users located to their left. We propose the Move to Right (MTR) policy, which scans from left to right assigning nearest rightmost available resource to a user, and contrast it to the Unidirectional Gale–Shapley (UGS) matching policy. While both policies among all unidirectional policies, minimize the expected distance traveled by a request (request distance), MTR is fairer. Moreover, we show that when user and resource locations are modeled by statistical point processes, and resources are allowed to satisfy more than one user, the spatial system under unidirectional policies can be mapped into bulk service queueing systems, thus allowing the application of many queueing theory results that yield closed form expressions. As we consider a case where different resources can satisfy different numbers of users, we also generate new results for bulk service queues. We also consider bidirectional policies where there are no directional restrictions on resource allocation and develop an algorithm for computing the optimal assignment which is more efficient than known algorithms in the literature when there are more resources than users. Numerical evaluation of performance of unidirectional and bidirectional allocation schemes yields design guidelines beneficial for resource placement. Finally, we present a heuristic algorithm, which applies the optimal dynamic programming scheme for one-dimensional inputs to obtain approximate solutions to the optimal assignment problem for the two-dimensional scenario and empirically yields request distances within a constant factor of the optimal solution.

Analysis of customer’s impatience on bulk service queueing system with unreliable server, setup time and two types of multiple vacation

In this investigation, we analyse the customer's impatience on unreliable bulk queueing system with two types of vacation. Depending upon the length of queue, the server is permitted to take two types of vacation called type I vacation and type II vacation. The server is possibly affected by breakdowns and takes considerable time for setup before the repair begins to start. After repair completion, the server will start its remaining service to the batch of customers whose service was interrupted. It could be assumed that the arriving units may be balked from the system when the server is on vacation (type I or type II). By incorporating the supplementary variables technique, the probability generating function of the queue size at an arbitrary and departure time epoch for the designed queueing system are derived. Finally, the stability condition, some performance measures, particular cases are obtained with appropriate numerical illustrations and graphical presentation.

Computational approach for transient behaviour of M/M (a, b)/1 bulk service queueing system with working vacation

A new computational technique is used to evaluate the Transient behaviour of Single Server Bulk Service Queueing System with Working Vacation with arrival rate λ which follows a Poisson process and the service will be in bulk. In this model the server provides two types of services namely normal service and lower service. The normal service time follows an exponential distribution with parameter μ1. The lower service rate follows an exponential distribution with parameter μ2. The vacation time follows an exponential distribution with parameter α. According to Neuts, the server begins service only when a minimum of ‘a’ customers in the waiting room and a maximum service capacity is ‘b’. An infinitesimal generator matrix is formed for all transitions. Time dependent solutions and Steady state solutions are acquired by using Cayley Hamilton theorem. Numerical studies have been done for Time dependent average number of customers in the queue, Transient probabilities of server in vacation and server busy for several values of t, λ, µ1, μ2, α, a and b.

An <i>M</i><SUP align="right">[<i>X</i>]</SUP>/<i>G</i>(<i>a</i>, <i>b</i>)/1 queue with unreliable server, second optional service, closedown, setup with N-policy and multiple vacation

Batch arrival bulk service queueing system has been effectively used to model many real life systems like production, manufacturing, transportation as well as telecommunication. Characteristic like second optional service, service interruption, closedown time, multiple vacation, setup time with N policy, etc. have been respectively considered in such models. So far, no comprehensive combination of these characteristics have been reported in the literature. This paper deals with the analysis of a non-Markovian batch arrival bulk service queue with a general combination of all the above mentioned characteristics.

Modelling and simulation analysis of a bulk queueing system

Purpose The purpose of this paper is to provide simulation modelling for bulk arrival bulk service queueing system involved in a textile industry and analyze the performance metrics. Design/methodology/approach This paper describes the simulation modelling of a bulk queueing system with limited number of admissions and multiple vacations. The model is developed for the proposed queueing system using Flexsim 2017, and it is explained through an application observed in a textile industry involving the process of cone winding. Findings In this paper, the simulation model has been developed to study the behaviour of queues at different resources in a production system. Various performance measures such as average components, average waiting time, total number of inputs and outputs, processing time and idle time involved in a textile industry are evaluated using simulation and justified through numerical illustration. Practical implications The proposed simulation model may be used in various scenarios wherever a real time situation exists related to bulk queueing system. The results produced in this paper can be used by the manufacturing industries to enhance the need-based accuracy. It is worth pointing out that the findings are of direct practical relevance and can be successfully used for a number of industrial applications. Originality/value The approach suggested in this paper attempts to deal with the queueing system involved in a textile industry and provides numerical results in less time with less computer resources. It provides a reasonably good approximation for simple and complex queueing models where it is difficult to find closed form of theoretical results.

An M^[X]/G(a,b)/1 queue with unreliable server, second optional service, closedown, setup with N-policy and multiple vacation

Batch arrival bulk service queueing system has been effectively used to model many real life systems like production, manufacturing, transportation as well as telecommunication. Characteristic like second optional service, service interruption, closedown time, multiple vacation, setup time with N policy, etc. have been respectively considered in such models. So far, no comprehensive combination of these characteristics have been reported in the literature. This paper deals with the analysis of a non-Markovian batch arrival bulk service queue with a general combination of all the above mentioned characteristics.

General bulk service queueing system with N-policy, multiplevacations, setup time and server breakdown without interruption

In this paper, we have considered an MX / (a,b) / 1 queueing system with server breakdown without interruption, multiple vacations, setup times and N-policy. After a batch of service, if the size of the queue is ξ (< a), then the server immediately takes a vacation. Upon returns from a vacation, if the queue is less than N, then the server takes another vacation. This process continues until the server finds atleast N customers in the queue. After a vacation, if the server finds at least N customers waiting for service, then the server needs a setup time to start the service. After a batch of service, if the amount of waiting customers in the queue is ξ (≥ a) then the server serves a batch of min(ξ,b) customers, where b ≥ a. We derived the probability generating function of queue length at arbitrary time epoch. Further, we obtained some important performance measures.

Discrete-Time Bulk Queueing System with Variable Service Capacity Depending on Previous Service Time

This paper considers a discrete-time bulk-arrival bulk-service queueing system with variable service capacity, where the service capacity varies depending on the previous service time. Using the supplementary variable method and the generating function technique, we obtain the queue length distributions at arbitrary slot boundaries and service completion epochs.

M/M(a, b)/(2,1) queueing system with servers repeated and delayed vacation

In queueing systems with multi-server models, every server goes on vacation irrespective of the availability of the server in the system. This creates inconvenience to the customers in places like computer network, communication network, hospitals, telegraph offices and telephone booths, etc., where at least one server must be available in the system for service. In this paper, an analysis has been carried out on a bulk service queueing system with two servers in which at least one server is available for service in the system always.

Non-Markovian bulk queueing system with state dependent arrivals and multiple vacations - a simulation approach

We considered a non-Markovian bulk arrival general bulk service queueing system with state dependent arrivals and multiple vacations in this paper. The arrivals occur in bulk with a rateλ, when the server is busy and with a rateλ0, when the server is on vacation. Using a supplementary variable technique and difference differential equations method we derive the queue size distribution, expected length of idle and busy periods and expected queue size of a Mx/G(a, b)/1 queueing system with state dependent arrivals and multiple vacations. We study the same through simulation using ARENA, a powerful manufacturing system simulation software and obtained some performance measures, which are mandatory for the study and analysis of the said queueing model. The simulated results for a few cases are presented.

Analysis of a MX/G(a,b)/1 queueing system with vacation interruption

In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a ’ customers waiting for service say ξ , he serves a batch of min (ξ , b) customers, where b ≥ a . On the other hand, if the queue length is at the most ‘a -1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary service, if the queue size reaches ‘a ’, during the secondary job period. On completion of the secondary job, the server remains in the system (dormant period) until the queue length reaches ‘a ’. For the proposed model, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is also developed. To optimize the cost, a numerical illustration is provided.

Queueing Delay Analysis for Multicast With Random Linear Coding

We analyze the queueing delay performance when random linear coding is performed over packets randomly arriving at a source node for multicast transmission over packet erasure channels. We model random coding of packets as a bulk-service queueing system, where packets are served and depart the queue in groups. In this framework, we analyze two different block-based random linear coding schemes. The first scheme involves coding over a fixed blocksize, which leads to simpler analysis but also to a delay penalty for lightly-loaded systems. The second scheme adapts to the traffic load by allowing for a variable blocksize, thereby removing the delay penalty at low loads. We provide results on the maximum stable arrival rate of packets at the source and on the queueing delay as a function of the arrival rate.

Modeling and analysis of TXOP differentiation in infrastructure-based WLANs

The Access Point (AP) is the bottleneck of infrastructure-based Wireless Local Area Networks (WLANs) due to its responsibility for forwarding all the incoming and outgoing frames. As a result, the network performance is significantly deteriorated by the unbalanced traffic loads at AP and other mobile stations. A potential solution to the bottleneck problem is to assign different Transmission Opportunity (TXOP) limits to the AP and mobile stations, respectively. This study develops a new analytical model to investigate the Quality-of-Service (QoS) performance metrics including throughput, total frame delay, and frame loss probability in infrastructure-based WLANs with TXOP differentiation under the unbalanced traffic loads. To this end, the transmission queue is modeled as a bulk service queueing system in order to address the challenge of queueing analysis arising from the TXOP burst transmission mechanism. The accuracy of this model is validated through extensive NS2 simulation experiments. The analytical results demonstrate that the implementation of TXOP differentiation can substantially alleviate the bottleneck effects of unbalanced traffic loads, increase the aggregate throughput and decrease the frame delay and loss probability. Moreover, the developed model can be adopted as a cost-efficient tool to evaluate the impact of TXOP limits on the network performance and to investigate the optimal setting of TXOP limits under different working conditions.

Analysis of a batch arrival general bulk service queueing system with variant threshold policy for secondary jobs

In this paper, a bulk service queueing system with variant threshold policy for secondary jobs is considered. On completion of service, if the queue length is less than ‘ a ’, the server performs a secondary job of type one, repeatedly, until the queue length reaches ‘ a ’. On returning from a secondary job of type one, if the queue length is at least ‘ a ’, the server performs another secondary job of type two, repeatedly, until the queue length reaches the threshold value ‘ N ’ ( N ≥ b > a ), then the server serves a batch of ‘b’ customers. Various performance measures and a cost model are presented.

Steady state analysis of a bulk arrival general bulk service queueing system with modified M-vacation policy and variant arrival rate

In this paper, a M X / G ( a , b )/1 queueing system with modified M-vacation policy and variant arrival rate is considered. After a service completion, if the number of waiting customers is less than a, then the server avails of multiple vacations till the queue length reaches a or consecutively avail of M number of vacations, whichever occurs first. After completing the Mth vacation, if the queue length is still less than a then the server remains in the system till it reaches a . The server starts the service only if the queue length