We consider the problem of how best to assign the service capacity in a queueing network in order to minimise the expected delay under a cost constraint. We study systems with several types of customers, general service time distributions, stochastic or deterministic routing, and a variety of service regimes. For such networks there are typically no analytical formulae for the waiting time dist...

Given a complete directed graph G = (V,E), the traveling repairman problem consists of determining a Hamiltonian circuit minimizing the sum of the waiting times of customers located at the nodes of the graph. In this paper, we propose two new linear integer formulations for TRP and computationally evaluate the strength of their linear programming relaxations. Computational results show the effi...

We study a system with unlimited service potential where all service requests are served in parallel. The entire system itself becomes unavailable for a random period of time at the first instance that the system becomes idle. A queue builds up while the system is unavailable, and then all waiting customers enter the system simultaneously-each to its own processor-when the system becomes availa...

Abstract: The present investigation deals with M/G/1 retrial queue with unreliable server and general retrial times. The server is subject to breakdowns and takes some setup time before starting the repair. The server renders first essential phase of service (FES) to all the arriving customers whereas second optional phase services (SOS) are provided after FES to only those customers who opt fo...

In this article, we present a continuous review perishable inventory systemwith a service facility. The service facility consists of a single server and a finite waiting room. If the arriving primary customer finds the waiting hall is empty and the server is idle, he immediately joins the service. The demanded items are issued by a server after some random time due to service on it. We assume t...

We derive the performance measures for non-priority customers in a priority single-server queue with two types of Markovian arrival processes (MAPs). One type of customers has preemptive resume (or repeat) priority over the other. We regard the model with two types of MAP arrivals as an MAP/SM/l queue with only non-priority customers arrivals, semi-Markovian service times and some server vacati...

We consider a randomized policy to control the M/G/1 queueing system with an unreliable server, second optional service and general startup times. The server is subject to breaking down according to a Poisson process, and the repair time obeys a general distribution. All arrived customers demand the first required service, and only some of the arrived customers demand the second optional servic...

We consider an open tandem queueing network with population constraint and constant service times. The total number of customers that may be presented in the network can not exceed a given value K. Customers arriving at the queueing network when there are more than K customers are forced to wait in an external queue. The arrival process to the queueing network is assumed to be arbitrary. We sho...

We consider the modelling of abandonment from a queueing system by impatient customers. Within the proposed model, customers act rationally to maximise a utility function that weights service utility against expected waiting cost. Customers are heterogeneous, in the sense that their utility function parameters may vary across the customer population. The queue is assumed invisible to waiting cu...