We derive the waiting time distribution in a GI/M/1 queueing system with dependence between the service time of each customer and the subsequent interarrival times. In addition, the server takes exponentially distributed vacations when there are no customers left to serve in the queue.

This paper deals with the optimal operation of a single removable and unreliable server in an Npolicy two-phase M/M/1 queueing system with gating, server startups and unpredictable breakdowns. Arrivals occur in batches according to a compound Poisson process and waiting customers receive batch service all at a time in the first phase and proceed to the second phase to receive individual service...

In this paper, we analyze a call center with impatient customers. We study how informing customers about their anticipated delays affects performance. Customers react by balking upon hearing the delay announcement, and may subsequently renege, particularly if the realized waiting time exceeds the delay that has originally been announced to them. The balking and reneging from such a system are a...

We consider a Markovian multiserver queueing model with time dependent parameters where waiting customers may abandon and subsequently retry. We provide simple uid and di usion approximations to estimate the mean, variance, and density for both the queue length and virtual waiting time processes arising in this model. These approximations, which are generated by numerically integrating only 7 o...

This paper considers a discrete-time queue with gated priority. Low priority customers arrive at the first queue at the gate in batches according to a batch Bernoulli process (BBP). When the gate opens, all low priority customers at the first queue move to the second queue at a single server. On the other hand, high priority customers directly join the second queue upon arrival. The arrival pro...

This paper is a contribution to the mathematical modeling of an important element in Ad hoc networks: Hello message. A queuing system is introduced to model the hello message receptions at given node. Here, the customers are the Hello messages and the service is defined as the processing of these messages. The modeling in question allows us to study the maximum waiting time of Hello messages be...

This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discrete Markovian service process. The server terminates service whenever the system becomes empty, and recommences service as soon as the number of waiting customers in the queue is N . We obtain the system-length distributions at prearrival and arbitrary epochs using the supplement...

This study examines a multiple-class M=G=1 queue with multiple thresholds. Each class of customer arrives according to an independent Poisson process, and each class has its own threshold. The idle server is reactivated as soon as any one of the thresholds is reached. Both FCFS and non-preemptive priority cases are considered. The Laplace–Stieltjes transform of the waiting time distribution fun...

This paper analyzes a discrete-time $Geo/Geo/c$ queueing system with multiple working vacations and reneging in which customers arrive according to a geometric process. As soon as the system gets empty, the servers go to a working vacations all together. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. Customer...

In this paper we consider a Jackson network of independent service stations. To improve upon the total expected waiting time, the stations may redistribute the total arrival rate of customers over all queues. We investigate this situation by means of arrival rate games. These are cooperative TU cost games in which the stations are the players and the total cost of a coalition is linear in the t...