a two server queueing system with single and batch service is considered in this paper. the arrival process is assumed to be poisson and the service rate follows an exponential distribution. server-i serves the customers in both single and batch service, while server-ii serves the customers in batch service only. the laplace transform of the transient and steady state behavior of the model is c...

In this paper we describe G/G/R+s multi- repairmen machining system with balking. The system consists of M operating machines, S spare machines, R permanent and s additional repairmen. Assuming the discrete flow of machines by continuous one, the diffusion approximation technique for the machine repair system has developed. The system will be in normal working mode if there is M operating machi...

The “Horizontal Y” shaped queuing model in which there is bulk infinite arrival of patients, but available M services are limited. discrete flow patients the system reduced continuous and a diffusion equation used. In terms means variances inter-arrival time distribution, this process number servers used, imposing reflecting boundaries. inspiration for analysis came from Aradhye Kallurkar [2], ...

The optimal control problem of adjusting the inflow, of piecewise constant type, to a supply chain in order to minimize the queue size and the quadratic difference between the outflow and the expected one is considered. The controls are represented by the duration of injections of different amounts of goods. The supply chain is modelled by a PDE-ODE: the conservation law describes the density o...

We consider the problems of online and stochastic packet queuing in a distributed system of n nodes with queues, where the communication between the nodes is done via a multiple access channel. In each round, an arbitrary number of packets can be injected into the system, each to an arbitrary node’s queue. Two measures of performance are considered: the total number of packets in the system, ca...

This paper reports a study on a single server queue with bulk arrival and bulk service patterns wherein the incoming traffic depends on the state of the server which may be in operating or breakdown state. The repair of the breakdown server is performed in two phases. The operating duration of server, repair duration of both phases of repairing as well as job's inter-arrival times and service t...

In this paper we consider a like-queue production system in which server startup and breakdowns are possible. The server is turned on (i.e. begins startup) when N units are accumulated in the system and off when the system is empty. We model this system by an M/M/1 queue with server breakdowns and startup time under the N policy. The arrival rate varies according to the server’s status: off, st...

In the Operations Research queue-joining literature, beginning with Naor (1969), the queue joining probability is monotonic decreasing in the queue length; the longer the queue, the fewer consumers join. Recent academic and empirical evidence indicates that queue-joining probabilities may not always be decreasing in the queue length. We provide a simple explanation for these non-monotonic queue...