Abhijit Datta Banik

Complete analysis of finite and infinite buffer GI/MSP/ 1 queue-A computational approach

We consider a finite buffer single server queue with renewal input and Markovian service process. System length distribution at pre-arrival and arbitrary epochs have been obtained along with some important performance measures. The corresponding infinite buffer queue has also been analyzed.

Complete analysis of MAP/G/1/N queue with single (multiple) vacation(s) under limited service discipline

We consider a finite-buffer single-server queue with Markovian arrival process (MAP) where the server serves a limited number of customers, and when the limit is reached it goes on vacation. Both single- and multiple-vacation policies are analyzed and the queue length distributions at various epochs, such as pre-arrival, arbitrary, departure, have been obtained. The effect of certain model parameters on some important performance measures, like probability of loss, mean queue lengths, mean waiting time, is discussed. The model can be applied in computer communication and networking, for example, performance analysis of token passing ring of LAN and SVC (switched virtual connection) of ATM.

BMAP/G/1/N queue with vacations and limited service discipline

Abstract We consider a finite buffer single server queue with batch Markovian arrival process ( BMAP ), where server serves a limited number of customer before going for vacation(s). Single as well as multiple vacation policies are analyzed along with two possible rejection strategies: partial batch rejection and total batch rejection. We obtain queue length distributions at various epochs and some important performance measures. The Laplace–Stieltjes transforms of the actual waiting time of the first customer and an arbitrary customer in an accepted batch have also been obtained.

Finite-Buffer Bulk Service Queue Under Markovian Service Process: GI/MSP (a,b)/1/N

Abstract We consider a single-server queue with renewal input and Markovian service process where server serves customers in batches according to a general bulk service rule. Queue length distributions at pre-arrival and arbitrary epochs have been obtained along with some important performance measures such as probability of blocking, mean queue lengths and mean waiting times. The analysis has been carried out assuming finite-buffer space for the arriving customers. The model has potential applications in areas such as computer networks, telecommunication systems and manufacturing systems.

An algorithmic analysis of the BMAP/MSP/1 generalized processor-sharing queue

This paper deals with the analysis of the BMAP/MSP/1 generalized processor-sharing queue. The analysis is based on RG-factorization technique applied to the Markov chain of the associated quasi-birth and death process. The stationary system-length distribution of the number of customers in the system and the LaplaceStieltjes transform (LST) of the sojourn time distribution of a tagged customer in the system is obtained in this paper. The mean sojourn time of a tagged customer is derived using the previous LST. The corresponding finite-buffer queueing model is also analyzed and system-length distribution is derived using the same technique as stated above. Further, the blocking probabilities for customers with different positions, such as the first-, an arbitrary- and the last-customer of a batch are obtained. The detail computational procedure for these models is discussed. Various numerical results are presented to show the applicability of the results obtained in the study. HighlightsAn infinite-buffer single server queue with batch Markovian arrival is considered.The service process is non-renewal as well under generalized processor sharing.Stationary system-length distribution is obtained using RG-factorization approach.The mean sojourn time of a tagged customer is analyzed in detail.Performance indices and blocking probability for finite-buffer are also obtained.

Finite buffer vacation models under E-limited with limit variation service and Markovian arrival process

We consider a finite-buffer single server queue with single (multiple) vacation(s) and Markovian arrival process. The service discipline is E-limited with limit variation (ELV). Several other service disciplines like, Bernoulli scheduling, nonexhaustive and E-limited service can be treated as special cases of the ELV service.

Stationary distributions and optimal control of queues with batch Markovian arrival process under multiple adaptive vacations

We consider an infinite-buffer single server queue with batch Markovian arrival process (BMAP) and exhaustive service discipline under multiple adaptive vacation policy. That is, the server serves until system emptied and after that server takes a random maximum number H different vacations until either he finds at least one customer in queue or the server have exhaustively taken all the vacations. The maximum number H of vacations taken by the server is a discrete random variable. We obtain queue-length distributions at various epochs such as, service completion/vacation termination, pre-arrival, arbitrary, post-departure and pre-service. The proposed analysis is based on the use of matrix-analytic procedure to obtain queue-length distribution at a post-departure epoch. Later we use supplementary variable method and simple algebraic manipulations to obtain the queue-length distribution at other epochs using queue-length distribution at post-departure epoch. Some important performance measures, like mean queue lengths and mean waiting times have been obtained. Several other vacation queueing models can be obtained as a special case of our model, e.g., single-, multiple-vacation model and queues with exceptional first vacation time. Finally, the total expected cost function per unit time is considered to determine a locally optimal multiple adaptive vacation policy at a minimum cost.

Analyzing state-dependent arrival in GI/BMSP/1/∞ queues

We consider an infinite-buffer single-server queue with renewal input. The service to the queueing system is provided in batches of random size, according to a batch Markovian service process (BMSP). The queue length distribution of the number of customers in the system at pre-arrival and arbitrary epochs has been obtained along with some important performance measures, such as the mean number of customers in the system and the mean system sojourn time of a customer. Secondly, we study a similar queueing system with queue-length-dependent inter-arrival times and obtain the above-mentioned state probabilities and performance measures. These queueing models have potential applications in the areas of computer networks, telecommunication systems, manufacturing systems, etc.

Equilibrium and Socially Optimal Balking Strategies in Markovian Queues with Vacations and Sequential Abandonment

In this paper, we consider customers’ equilibrium and socially optimal behavior in a single-server Markovian queue with multiple vacations and sequential abandonments. Upon arrival customers decide for themselves whether to join or balk, based on the level of information available to them. During the server’s vacation, present customers become impatient and decide sequentially whether they will abandon the system or not upon the availability of a secondary transport facility. Assuming the linear reward-cost structure, we analyze the equilibrium balking strategies of customers under four cases: fully and almost observable as well as fully and almost unobservable. In all the above cases, the individual and social optimal strategies are derived. Finally, the dependence of performance measures on system parameters are demonstrated via numerical experiments.

Equilibrium behaviour and social optimization in Markovian queues with impatient customers and variant of working vacations

We study customers’ equilibrium behaviour and social optimization in a single-server Markovian queue with impatient customers and variant of multiple working vacations, where the impatience is due to slow service rate. Under the variant of multiple working vacations, the server takes a working vacation as soon as the system gets empty. When an arriving customer joins the vacation system, it activates an impatience timer. If its patience timer expires before it gets service, the customer abandons the system, and never returns. The server is allowed to take at most J successive working vacations, if at the end of a working vacation the system remains empty. An arriving customer takes a decision on the basis of available information whether to join or to balk, which unifies wish for the service as well as reluctance to wait. We discuss equilibrium threshold strategies on the basis of linear reward-cost structure in the fully observable and fully unobservable cases. We present numerical results that establish the impact of the information level as well as various parameters on the equilibrium balking strategies and social benefits. The research outputs may be useful for decision makers to convey information to customers in net benefit maximization and for examining the corresponding social optimization problems.