Bulk Queueing Research Articles

A bulk queue’s analysis with two-stage heterogeneous services, multiple vacations, closedown with server breakdown, and two types of renovation

A queueing system with two stages of heterogeneous services, multiple vacations, and closedown upon server failure is considered in this study for MX/Ga,b data. Two different services must be provided to a group of customers one at a time. At time C, the server finishes its shut-down procedures following the conclusion of each SPS. A server that has a queue length shorter than a takes numerous, different-duration vacations. Upon returning from vacation, if the server detects that there are less than a customers in the queue, they will continue to serve the following batch if the server determines that there are at least a customers waiting for service. During the server’s first phase of operation, the service channels will momentarily fail with a probability of (π1) at any time, and during the server’s second phase of operation, the service channels will fail with a probability of (π2) at any time.

Cost benefit analysis for non-Markovian bulk queue with server failure

Cost benefit analysis for non-Markovian bulk queue with server failure

A State Dependent Arrival Analysis In a Non-Markovian Bulk Queue with Server Failures

A State Dependent Arrival Analysis In a Non-Markovian Bulk Queue with Server Failures

Cost Benefit Analysis for Non-Markovian Bulk Queue with Server Failure

Cost Benefit Analysis for Non-Markovian Bulk Queue with Server Failure

Modeling of Communication Network with Queuing Theory under Fuzzy Environment

In the present study, quantitative model and methods that analyze dynamic system of communication flow have been developed in the domain of queuing theory under uncertain environment. The study approach supports model-based queue design as opposed to creative engineering. Some critical aspects and results of queue model and fuzzy set theory has been reviewed in brief and the application of bulk queue model to communication network under imprecise data has been discussed. We have assumed that the arrival pattern, service pattern as well covariance between incoming and transmitted packets all are fuzzy in nature. The system characteristics with defuzzification process have been explored on the basis of lower and upper bound at possibility level alpha and signed distance method. The validity of the results has been analyzed through numerical illustration and graphical study.

Developing bulk arrival queuing models with the constant batch policy under uncertainty data using (0 - 1) variables

This paper delves into some significant performance measures (PMs) of a bulk arrival queueing system with constant batch size b, according to arrival rates and service rates being fuzzy parameters. The bulk arrival queuing system deals with observation arrival into the queuing system as a constant group size before allowing individual customers entering to the service. This leads to obtaining a new tool with the aid of generating function methods. The corresponding traditional bulk queueing system model is more convenient under an uncertain environment. The $alpha$-cut approach is applied with the conventional Zadeh's extension principle (ZEP) to transform the triangular membership functions (Mem. Fs) fuzzy queues into a family of conventional bulkqueues. This new model focus on mixed-integer non-linear programming (MINLP) tenders a mathematical computational approach is known as (0 -1) variables. To measures the efficiency of the method, the efficient solution strategy plays a crucial role in the adequate application of these techniques. Furthermore, different stages of the $alpha$-cut intervals were analyzed and the final part of the article gives a numerical solution of the proposed model to achieve practical issues.

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.

Analysis of unreliable bulk queueing system with overloading service, variant arrival rate, closedown under multiple vacation policy

Analysis of unreliable bulk queueing system with overloading service, variant arrival rate, closedown under multiple vacation policy

Bernoulli vacation model for MX/G/1 unreliable server retrial queue with bernoulli feedback, balking and optional service

The study of unreliable server retrial bulk queue with multiphase optional service is analyzed by incorporating the features of balking, Bernoulli vacation and Bernoulli feedback. On the occasion when the server is occupied with the service of the customers, an arriving customer finding the long queue, can join the retrial orbit and receives its service later on by making re-attempt. The system is reinforced with multi phase optional service along with essential service and joining customer can opt any one of optional services after getting essential service. Furthermore, the essential/optional service can be aborted due to abrupt failure of the server. There is an immediate support of multi phase repair facility to take care of the failed server, but sometimes repair may be put on hold by virtue of any unexpected cause. If the service is unsatisfactory, the customer can rejoin the queue as feedback customer. Bernoulli vacation is permitted to the server following the respective busy period. For evaluating the queue size distribution and other system performance metrics, supplementary variable technique (SVT) is used. The approximate solutions for the steady state probabilities and waiting time are suggested using maximum entropy principle (MEP). We perform a comparative study of the exact waiting time obtained by the supplementary variable technique and the approximate waiting time derived by using maximum entropy principle by taking the numerical illustration. Quasi Newton method is used to find optimal cost. To verify the outcomes of the model, numerical illustrations and senstivity analysis have been accomplished.

Analysis of unreliable bulk queueing system with overloading service, variant arrival rate, closedown under multiple vacation policy

Analysis of unreliable bulk queueing system with overloading service, variant arrival rate, closedown under multiple vacation policy

Analysis of tri-cum biserial bulk queue model connected with a common server

The present paper demonstrates the tri-cum biserial bulk queue model linked with a common server with fixed batch size. The development of the model has been done in the steady-state condition. The arrival and servicing patterns of the customers are postulated to follow the Poisson law. Various queuing model performances have been assessed by using the probability generating function technique and other statistical tools. The broad parametric examination has been documented to show the adequacy of the current arrangement procedure.

(p,N)-Policy for Unreliable Server Bulk Queue with Bernoulli Feedback

In the present study, we investigate a bulk arrival queue with Bernoulli feedback, service interruption and having the facility of multi-phases essential/optional services. If units present in the system are accumulated to $$ N, $$ the server is switched on so that it may start service with probability $$ p, $$ or it remains switched off with probability $$ 1 - p $$ . There is a provision to avail the vacation schedule by the server as soon as the system becomes empty. After returning from vacation if the system size is more than $$ N, $$ the server immediately starts serving the units waiting in the queue. During one of the stages of the service, the server may become inoperative due to some fault; in such a scenario it will undergo for repair with a probable situation leading to delayed repair due to unforeseen reasons. Supplementary variable technique (SVT) is employed for queueing analysis and to derive various performance measures characterizing the delay and service interruption. Some reliability indices and cost function are established for the concerned model. SVT is exhibited by taking numerical illustration.

Analysis of Repairable Single Server Bulk Queue with Standby Server, Two Phase Heterogeneous Service, Starting Failure and Multiple Vacation

Analysis of Repairable Single Server Bulk Queue with Standby Server, Two Phase Heterogeneous Service, Starting Failure and Multiple Vacation

Analysis of bulk queue with unreliable service station, second optional repair, N-policy multiple vacation, loss and immediate feedback in production system

In this paper an unreliable server bulk service queue with second optional repair, multiple vacation under N-policy, customer's feedback and impatience are considered. After finishing a service, the server avails a multiple vacation under N-policy only when the queue length is less than 'a'. Server vacation models are very much useful for a queueing system in which server needs to utilise his idle time for a different purpose. The server is subject to breakdown during the service and requires second optional repair for restoration. After repair completion, the server will start its remaining service to the batch of customers whose service was interrupted. Further, it is assumed that the arriving units may balk (loss) from the system when the server is on vacation and immediate feedback service was provided to the dissatisfied customers. The queue size distribution at a random and departure epoch has been derived using the supplementary variable technique. Finally, the stability condition, some performance measures, particular cases and numerical results of the proposed model are obtained.

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.

Numerical Study on Transient Behaviour of Finite Bulk Arrival or Service Queues with Multiple Working Vacations

The transient behaviour of single server bulk queues with finite-buffer capacity is discussed numerically under the assumption that the server may take multiple working vacations after completing a busy period. It is considered that the inter-arrival and the service times are exponentially distributed and independent of each other. The buffer space is limited, therefore partial and full batch rejection policies are studied for the bulk arrival queueing model. However, for the batch service, the general bulk service rule is considered. Using probabilistic arguments and relating the state of the systems at two consecutive time epochs, differential equations are obtained to model such phenomena. Further, these equations are solved numerically by Runge-Kutta method and the time dependent numerical solutions are compared with the exact stationary solutions. The blocking probability and the mean waiting time of the first, last and an arbitrary customer are also reviewed mathematically and computed numerically.

Analysis of tri-cum biserial bulk queue model connected with a common server

The present paper demonstrates the tri-cum biserial bulk queue model linked with a common server with fixed batch size. The development of the model has been done in the steady-state condition. The arrival and servicing patterns of the customers are postulated to follow the Poisson law. Various queuing model performances have been assessed by using the probability generating function technique and other statistical tools. The broad parametric examination has been documented to show the adequacy of the current arrangement procedure.

Cost optimisation and maximum entropy analysis of a bulk queueing system with breakdown, controlled arrival and multiple vacations

This article analyses a bulk queueing system with multiple vacations, controlled arrival and breakdown. The service is done in bulk with a minimum of 'a' customers and a maximum of 'b' customers. The server is assigned for secondary jobs (vacations) repeatedly when the number of customers is inadequate to process. The arrivals are accepted with a probability α, β and γ during the busy, vacation and renovation period respectively. During a batch service, if the server breaks down with probability π, the service for the particular batch is processed without interruption. Upon completion of service, the renovation of service station will be considered. The probability generating function for the queue size at an arbitrary time epoch is derived. Various performance measures are obtained. A few particular cases are discussed. Maximum entropy analysis is carried out and validated through numerical illustration. The cost model is also developed to optimise the cost.

Analysis of bulk queue with unreliable service station, second optional repair, N-policy multiple vacation, loss and immediate feedback in production system

In this paper an unreliable server bulk service queue with second optional repair, multiple vacation under N-policy, customer's feedback and impatience are considered. After finishing a service, the server avails a multiple vacation under N-policy only when the queue length is less than 'a'. Server vacation models are very much useful for a queueing system in which server needs to utilise his idle time for a different purpose. The server is subject to breakdown during the service and requires second optional repair for restoration. After repair completion, the server will start its remaining service to the batch of customers whose service was interrupted. Further, it is assumed that the arriving units may balk (loss) from the system when the server is on vacation and immediate feedback service was provided to the dissatisfied customers. The queue size distribution at a random and departure epoch has been derived using the supplementary variable technique. Finally, the stability condition, some performance measures, particular cases and numerical results of the proposed model are obtained.

Cost optimisation and maximum entropy analysis of a bulk queueing system with breakdown, controlled arrival and multiple vacations

This article analyses a bulk queueing system with multiple vacations, controlled arrival and breakdown. The service is done in bulk with a minimum of 'a' customers and a maximum of 'b' customers. The server is assigned for secondary jobs (vacations) repeatedly when the number of customers is inadequate to process. The arrivals are accepted with a probability α, β and γ during the busy, vacation and renovation period respectively. During a batch service, if the server breaks down with probability π, the service for the particular batch is processed without interruption. Upon completion of service, the renovation of service station will be considered. The probability generating function for the queue size at an arbitrary time epoch is derived. Various performance measures are obtained. A few particular cases are discussed. Maximum entropy analysis is carried out and validated through numerical illustration. The cost model is also developed to optimise the cost.