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In this paper, we analyse a single server preemptive priority queue with phase-type vacation and repair, feedback, working breakdown, close-down and impatient customers. Customers arrive according to the Marked Markovian Arrival Process and their service time according to Phase-type distribution. If the High Priority customers need feedback, they lose their priority and join the Low Priority queue. At any instant, if the server is broken down, the server provide service with slow mode for that current customer and then the server will go into a repair process. When there are no customers present in both the queues, the server close-down the system and then goes on vacation. During the close-down and vacation period, high priority customers may balk. The Matrix Analytic Method is used to look into the number of consumers that are currently in the system. Analysis of the steady-state, the server active period, and the total cost are all discussed. Finally, some significant performance measures and numerical examples are given. [ABSTRACT FROM AUTHOR]

This paper deals with a M/M/c queueing system with waiting servers, balking, reneging, and K-variant working vacations subjected to Bernoulli schedule vacation interruption. Whenever the system is emptied, the servers wait for a while before synchronously going on vacation during which services are offered with a lower rate. We obtain the steady-state probabilities of the system using the matrix-geometric method. In addition, we derive important performance measures of the queueing model. Moreover, we construct a cost model and apply a direct search method to get the optimum service rates during both working vacation and regular working periods at lowest cost. Finally, numerical results are provided. [ABSTRACT FROM AUTHOR]

Among the waiting models proposed in the literature most of them focus on homogeneous arrival rate. This paper proposes a single server waiting line with modulated arrival rate of small and large size of traffic sources. Modulation of arrival rate induces the server to shift the service rate that follow phase type distribution. Using Neut's versatile point process under quasi birth death environment we present the steady state analysis of the system. We provide examples numerically to perform the results and represent it in graphical form. [ABSTRACT FROM AUTHOR]

The queueing systems with a fixed batch size are commonly discussed in literatures. However, most real-life systems involve multiple types of servers with varying service capacities. To characterize this feature, random service capacity is considered in a double-ended queueing system in this paper, in which an arrival server can serve at most k customers with probability α k. Customers' threshold strategies are discussed based on the conditional expected waiting time and customers' beliefs in the number of servers in the orbit. Then, stationary analyses are conducted for this double-ended queueing system with random service capacity and balking customers, which includes establishing a sufficient stability condition, calculating the stationary distribution for system states and stationary performance measures. Finally, numerical examples are presented to explore how performance measures are influenced by system parameters. [ABSTRACT FROM AUTHOR]

In this paper, we study a limited clearing queueing model with an orbit and non-persistent customers, in which the space of service station is finite and the server can serve all customers in the service station simultaneously. If a customer (new arrival or retrial) finds the station is full, he/she will decide whether join the orbit or not with respective probabilities. We first analyze the necessary and sufficient condition for the stability of this system, then using matrix geometric analytic method and spectral expansion method, we obtain the stationary distribution of this model. Besides, we also give many important performance measures of this system which help managers to make wisdom managerial decisions and designs, such as the mean size of service station, the mean queue length of the orbit and the mean sojourn time of an arbitrary customer. Finally, some numerical examples are provided to show the impacts of various parameters on the system performance measures. [ABSTRACT FROM AUTHOR]

We consider Markovian multiserver retrial queues where a blocked customer has two opportunities for abandonment: at the moment of blocking or at the departure epoch from the orbit. In this queueing system, the number of customers in the system (servers and buffer) and that in the orbit form a level-dependent quasi-birth-and-death (QBD) process whose stationary distribution is expressed in terms of a sequence of rate matrices. Using a simple perturbation technique and a matrix analytic method, we derive Taylor series expansion for nonzero elements of the rate matrices with respect to the number of customers in the orbit. We also obtain explicit expressions for all the coefficients of the expansion. Furthermore, we derive tail asymptotic formulas for the joint stationary distribution of the number of customers in the system and that in the orbit. Numerical examples reveal that the tail probability of the model with two types of nonpersistent customers is greater than that of the corresponding model with one type of nonpersistent customers. They also reveal that the series expansion with a few terms can be used to obtain an accurate approximation to the stationary distribution. [ABSTRACT FROM AUTHOR]

In this paper, we consider a continuous review perishable inventory system wherein demands arrive according to the Poisson process, each demanding exactly one unit of inventory item and the life time of each item is assumed to be exponential. The operating policy is ( s, S ) policy, i.e., whenever the inventory level drops to s , an order for Q (= S − s ) items is placed. The ordered items are received after a random time which is distributed as exponential. The service may be interrupted according to the Poisson process in which case it restarts after an exponentially distributed time. The demands that occur during the server breakdown period or stock-out period may turn out to be ordinary or a negative demand and then they enter into the orbit of infinite size. These orbiting demands send out a signal to compete for their demand which is distributed as exponential. The matrix analytic method is used for the steady state distribution of the model. Various performance measures and cost analysis are shown with numerical results. [ABSTRACT FROM AUTHOR]

We consider a service system with two types of customers. In such an environment, the servers can either be specialists (or dedicated) who serve a specific customer type, or generalists (or flexible) who serve either type of customers. Cross-trained workers are more flexible and help reduce system delay, but also contribute to increased service costs and reduced service efficiency. Our objective is to provide insights into the choice of an optimal workforce mix of flexible and dedicated servers. We assume Poisson arrivals and exponential service times, and use matrix-analytic methods to investigate the impact of various system parameters such as the number of servers, server utilization, and server efficiency on the choice of server mix. We develop guidelines for managers that would help them to decide whether they should be either at one of the extremes, i.e., total flexibility or total specialization, or some combination. If it is the latter, we offer an analytical tool to optimize the server mix. [ABSTRACT FROM AUTHOR]