Analysis of classical retrial queue with differentiated vacation and state dependent arrival rate.

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

An M^x/G(a,b)/1 queue with breakdown and delay time to two phase repair under multiple vacation

In this paper, we consider an Mx /G(a,b)/1 queue with active breakdown and delay time to two phase repair under multiple vacation policy. A batch of customers arrive according to a compound Poisson process. The server serves the customers according to the “General Bulk Service Rule” (GBSR) and the service time follows a general (arbitrary) distribution. The server is unreliable and it may breakdown at any instance. As the result of breakdown, the service is suspended, the server waits for the repair to start and this waiting time is called as „delay time‟ and is assumed to follow general distribution. Further, the repair process involves two phases of repair with different general (arbitrary) repair time distributions. Immediately after the repair, the server is ready to start its remaining service to the customers. After each service completion, if the queue length is less than \u27a\u27, the server will avail a multiple vacation of random length. In the proposed model, the probability generating function of the queue size at an arbitrary and departure epoch in steady state are obtained using the supplementary variable technique. Various performance indices, namely mean queue length, mean waiting time of the customers in the queue etc. are obtained. In order to validate the analytical approach, we compute numerical results

Non-Markovian Queueing System, Mx/G/1 with Server Breakdown and Repair Times

This paper deals with the steady state behavior of an MX/G/1 queue with breakdown. It assumed that customers arrive to the system in batches of variable size, but serve one by one. The main new assumption in this paper is that the repair process does not start immediately after a breakdown and there is a delay time waiting for repairs to start. We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average waiting time in the queue

Transient behavior of M[x]/G/1 Retrial Queueing Model with Non Persistent Customers, Random break down, Delaying Repair and Bernoulli Vacation

In this paper we consider a single server batch arrival non-Markovian retrial queueing model with non persistent customers. In accordance with Poisson process, customers arrive in batches with arrival rate  and are served one by one with first come first served basis. The server is being considered as unreliable that it may encounter break down at any time. In order to resume its service the server has to be sent for repair, but the repair does not start immediately so that there is a waiting time before the repair process. The customer, who finds the server busy upon arrival, can either join the orbit with probability p or he/she can leave the system with probability 1-p. More details can be found in the full paper. Key words: Batch size, break down, delay time, transient solution, steady solution,  reliability indices

HETEROGENEOUS SERVER RETRIAL QUEUEING MODEL WITH FEEDBACK AND WORKING VACATION USING ARTIFICIAL BEE COLONY OPTIMIZATION ALGORITHM

This research delves into the dynamics of a retrial queueing system featuring heterogeneous servers with intermittent availability, incorporating feedback and working vacation mechanisms. Employing a matrix geometric approach, this study establishes the steady-state probability distribution for the queue size in this complex heterogeneous service model. Additionally, a range of system performance metrics is developed, alongside the formulation of a cost function to evaluate decision variable optimization within the service system. The Artificial Bee Colony (ABC) optimization algorithm is harnessed to determine service rates that minimize the overall cost. This work includes numerical examples and sensitivity analyses to validate the model's effectiveness. Also, a comparison between the numerical findings and the neuro-fuzzy results has been examined by the adaptive neuro fuzzy interface system (ANFIS)

HETEROGENEOUS SERVER RETRIAL QUEUEING MODEL WITH FEEDBACK AND WORKING VACATION USING ARTIFICIAL BEE COLONY OPTIMIZATION ALGORITHM

This research delves into the dynamics of a retrial queueing system featuring heterogeneous servers with intermittent availability, incorporating feedback and working vacation mechanisms. Employing a matrix geometric approach, this study establishes the steady-state probability distribution for the queue size in this complex heterogeneous service model. Additionally, a range of system performance metrics is developed, alongside the formulation of a cost function to evaluate decision variable optimization within the service system. The Artificial Bee Colony (ABC) optimization algorithm is harnessed to determine service rates that minimize the overall cost. This work includes numerical examples and sensitivity analyses to validate the model’s effectiveness. Also, a comparison between the numerical findings and the neuro-fuzzy results has been examined by the adaptive neuro fuzzy interface system (ANFIS)

A Multi-Server Retrial Queueing Inventory System With Asynchronous Multiple Vacations

This article deals with asynchronous server vacation and customer retrial facility in a multi-server queueing-inventory system. The Poisson process governs the arrival of a customer. The system is comprised of c identical servers, a finite-size waiting area, and a storage area containing S items. The service time is distributed exponentially. If each server finds that there are an insufficient number of customers and items in the system after the busy period, they start a vacation. Once the servers vacation is over and it recognizes there is no chance of getting busy, it goes into an idle state if the number of customers or items is not sufficient, otherwise, it will take another vacation. Furthermore, each server's vacation period occurs independently of the other servers. The system accepts a (s, Q) control policy for inventory replenishment. For the steady state analysis, the Marcel F Neuts and B Madhu Rao matrix geometric approximation approach is used owing to the structure of an infinitesimal generator matrix. The necessary stability condition and R matrix are to be computed and presented. After calculating the sufficient system performance measures, an expected total cost of the system is to be constructed and numerically incorporated with the parameters. Additionally, numerical analyses will be conducted to examine the waiting time of customers in the queue and in orbit, as well as the expected rate of customer loss.Comment: 43 pages, 12 figures, 5 table

Performance Analysis of a Retrial Queueing System with Optional Service, Unreliable Server, Balking and Feedback

This paper considers a Markovian retrial queueing system with an optional service, unreliable server, balking and feedback. An arriving customer can avail of immediate service if the server is free. If the potential customer encounters a busy server, it may either join the orbit or balk the system. The customers may retry their request for service from the orbit after a random amount of time. Each customer gets the First Essential Service (FES). After the completion of FES, the customers may seek the Second Optional Service (SOS) or leave the system. In the event of unforeseen circumstances, the server may encounter a breakdown, at which point an immediate repair process will be initiated. After the service completion, the customer may leave the system or re-join the orbit if not satisfied and demand regular service as feedback. In this investigation, the stationary queue size distributions are framed using a recursive approach. Various system performance measures are derived. The effects induced by the system parameters on the performance metrics are numerically and graphically analysed

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"