In this paper, a bulk arrival general bulk service queueing model delayed service with restricted vacation policy, variant arrival rate and setup time is considered. The server starts the service only if at least ‘a’ customers are waiting in the queue, and renders the service according to the general bulk service rule with minimum of ‘a’ customers and maximum of ‘b’ customers, then the server w...

We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-l customer who, upon his arrival, meets k customers already present in the SMP/M/1/PS queue is identi...

conclusions using the simulation as a decision making tool helps us to decide how we can reduce outpatient's waiting time. comparison of outputs of this scenario and the based- case scenario in simulation model shows that combining physician's work time changing with patient's admission time changing (scenario 9) would reduce patient waiting time about 73.09%. due to dynamic and complex nature ...

We consider the waiting time distribution of the Gl/Gl /1 queue where customers are served in random order; inter-arrival and service times may have finite or infinite variance. Our main result shows that the waiting time in heavy traffic can be written as a product of two random variables. Our proof is based on the intuitively appealing fact that in heavy traffic, the queue length stays consta...

We consider a single-server queue subject to multiple types of operation-independent and class-dependent interruptions motivated by operations and vessel queueing at entrances of waterways. A case in point is the Istanbul Strait. We are using waiting-time arguments and service completion time analysis to obtain the expected waiting time of a customer (vessel) in the aforementioned queue with tw...

We introduce a new approach to modelling queueing systems where the priority or the routing of customers depends on the time the first customer has waited in the queue. This past waiting time of the first customer in line, W, is used as the primary variable for our approach. A Markov chain is used for modelling the system where the states represent both the number of free servers and a discrete...

In this paper, we study the dynamic pricing problem of a multi-server facility that processes requests from several customer classes on a first come first served basis. We assume an arrival belongs to one of a finite number of customer classes and that each class is distinguished by known and arbitrary service valuations and arbitrary but non-decreasing waiting cost functions. We model the faci...

A queue is a waiting line (like customers waiting at a supermarket checkout counter); queueing theory is the mathematical theory of waiting lines. More generally, queueing theory is concerned with the mathematical modeling and analysis of systems that provide service to random demands. A queueing model is an abstract description of such a system. Typically, a queueing model represents (1) the s...

We consider an M/G/1 retrial queue with general retrial times and single working vacation. During the working vacation period, customers can be served at a lower rate. Both service times in a vacation period and in a service period are generally distributed random variables. Using supplementary variable method we obtain the probability generating function for the number of customers and the ave...

A system with several queues is considered. Each queue has a server with exponential servicetime with same service rate. Normal customers arrive at the system and choose which queue to join. Theyare supposed to join the shortest queue. Special customers also arrive at the system though the arrivals arerare. They can also choose which queue to join and they have other options, waitin...