We consider a polling system with two queues, exhaustive service, no switch-over times and exponential service times with rate μ in each queue. The waiting cost depends on the position of the queue relative to the server: It costs a customer c per time unit to wait in the busy queue (where the server is) and d per time unit in the idle queue (where no server is). Customers arrive according to a...

This paper presents a decision model that uses empirical Bayesian estimation to construct a server-dependent M/M/2/L queuing system. A Markovian queue with a number of servers depending upon queue length with finite capacity is discussed. This study uses the number of customers for initiating and turning off the second server as decision variables to formulate the expected cost minimization mod...

——In this paper we study an optimal server allocation problem, where a single server is shared among multiple queues based on the queue backlog information. Due to the physical nature of the system this information is delayed, in that when the allocation decision is made, the server only has the backlog information from an earlier time. Queues have different arrival processes as well as differe...

An embedded Markov chain is used to analyze a G/M/1 queuing system with N policy. When the system is empty, the server remains idle (deactivates) and does not start serving the waiting customers in the queue until the number of arrivals reaches N. The service is performed in batches of min(n, N) if there are n customers waiting at the completion of service. Service times of the server depend o...

Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps track of the residual service times of all jobs in the system at any given time. From this measure valued process, one can recover the traditional performance ...

In this paper we analyze a single server queue with batch arrival Poisson input, two heterogeneous service with different general (arbitrary) service time distributions and two phase (compulsory and optional) server vacations with general (arbitrary) vacation period. The first phase of service is essential for all customers, as soon as the first service of a customer is completed, then with pro...

This paper shows that in the G/M/1 queueing model, conditioning on a busy server, the age of the inter-arrival time and the number of customers in the queue are independent. Explicit expressions for the density functions of this age conditioning on a busy server and conditioning on an idle server are given. Moreover, we show that this independence property, which we prove by elementary argument...

Abstract. We consider a two-priority, preemptive, single-server queueing model. Each customer is classified into either a high priority class or a low priority class. The arrivals of the two priority classes follow independent Poisson processes and service time is assumed to be exponentially distributed. A queue-length-cutoff method is considered. Under this discipline the server responds only ...

The paper provides the upand down-crossing method to study the asymptotic behavior of queue-length and waiting time in closed Jackson-type queueing networks. These queueing networks consist of central node (hub) and k single-server satellite stations. The case of infinite server hub with exponentially distributed service times is considered in the first section to demonstrate the upand down-cro...

This paper studies load balancing for many-server (N servers) systems. Each server has a buffer of size b − 1, and can have at most one job in service 1 jobs the buffer. The time follows Coxian-2 distribution. We focus on steady-state performance policies heavy traffic regime such that normalized system is λ = N−α 0 < α 0.5. identify set achieve asymptotic zero waiting. include several classica...