We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. This assumption implies that o -periods in the arrival process are i.i.d. and geometrically distributed. For this queue, we establish the exact relationship between queue length distributions in a nite-bu...

Abstract: The purpose of this research is to develop algorithm calculating the traffic queue length which is main variable for effective operation at signalized intersection. For the methods to calculate the traffic queue length, there are queue theory and shock wave theory. And, the estimation of traffic queue length by existing point detection system utilizes traffic queue theory calculating ...

The so-called “Israeli queue” (Boxma et al. in Stoch Model 24(4):604– 625, 2008; Perel and Yechiali in Probab Eng Inf Sci, 2013; Perel and Yechiali in Stoch Model 29(3):353–379, 2013) is a multi-queue polling-type system with a single server. Service is given in batches, where the batch sizes are unlimited and the service time of a batch does not depend on its size. After completing service, th...

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there are no customers in the system, the server takes vacation consisting of K -phases, each phase is generally distributed. Here the first phase is compulsory where as the other phases are optional. For this model the supplementary var...

Machines whose sole function is to re-order their input data are considered. Every such machine defines a set of allowable input-output pairs of permutations. These sets are studied in terms of the minimal disallowed pairs (the basis). Some allowable sets with small bases are considered including the one defined by a priority queue machine. For more complex machines defined by two or more prior...

In a single server polling system, the server visits the queues according to a routing policy and while at a queue serves some or all of the customers there according to a service policy. A polling (or scheduling) policy is a sequence of decisions on whether to serve a customer, idle the server, or switch the server to another queue. The goal of this paper is to nd polling policies that stochas...

We develop a queueing model for an appointment-based service system that consists of two queues in tandem: the appointment queue followed by the service queue. Customers join the appointment queue when they call for appointments, stay there (not physically) until the appointment time comes, and then leave the appointment queue and may physically join the service queue, and wait there until serv...