Abstract: A Poisson stream of customers arrives at a service center which consists of two single-server queues in parallel. The service times of the customers are exponentially distributed, and both servers serve at the same rate. Arriving customers join the shortest of the two queues, with ties broken in any plausible manner. No jockeying between the queues is allowed. Employing linear programming techniques, we calculate bounds for the probability distribution of the number of customers in the system, and its expected value in equilibrium. The bounds are asymptotically tight in heavy traffic.

Abstract: A general class of vehicle dispatching strategies for bulk arrival, bulk service queues is examined which consist of some combination of vehicle holding and cancellation strategies. The moments of the length of the queue at vehicle departure instants and in continuous time are solved for exactly using transform methods. Relationships between the moments of the waiting time and queue length distributions are developed without further use of transforms, resulting in an exact expression for the expected waiting time and an approximation for the variance. A simple approach for calculating the roots of a particular function, needed to find the moments of the queue length distribution, is presented and used to demonstrate that this task can be accomplished very easily. Finally, the model is used to compare alternative vehicle dispatching strategies in terms of costs and levels of service.

Abstract: This paper considers a districting problem for a demand-responsive service system in which queuing is allowed. Customers, located at the nodes of a transportation network, call in a Poisson manner, asking for on-scene service by a mobile service unit. Two such units service the entire network, with unit i(i = 1, 2) responsible for all nodes Ni in its unique “service territory.” In response to a call from within Ni, unit i, if available, is dispatched immediately to the customer; if the unit is busy with a previous customer, the call is dispatched in a FIFO manner. Each service territory, with its response unit, behaves as an independently operating M/G/1 queuing system. The problem addressed in this paper is determination of the optimal service territories, given fixed home locations for each of the service units, so as to minimize the average response time (queuing delay plus travel time) to a random customer. Exact results are obtained for limiting values of demand rate, and efficient heuristics are pre...

Abstract: This paper stresses the usefulness of developing a metamodel as an auxilliary model in simulation analysis and emphasizes the importance of validating the metamodel in order to determine whether it accurately approximates the simulation-generated data. A simulation model of the M/M/s queuing system was used for demonstration purposes. Two statistical validation procedures appropriate for simulation metamodels were discussed and demonstrated: use of a holdout sample and double cross- validation. The metamodel developed from the M/M/s queuing system simulation data proved to be valid as an approximation not only to the simulation but also to the real-world system itself.

Abstract: In many data communication and telephone switching systems, one processor must perform more than one type of task. In some systems it is advantageous to place the different tasks in different queues and have the processor serve the queues in a cyclic manner. Moreover, the system design often imposes a (finite or infinite) limit on the number of entries that may be served per cycle from any given queue; this limit typically varies from queue to queue. This paper will derive the capacity estimation of such systems. We consider systems which, in addition to serving n queues cyclically, must execute maintenance (or other low-priority jobs) without severely disrupting the queues' performance. For two alternative methods of scheduling the maintenance, we compute steady state values of i) the average cycle time, ii) the average number of entries of each queue served per cycle, iii) the average time spent at each queue per cycle, iv) the average amount of elapsed time necessary to complete a given amount of maintenance execution real time, and v) if the arrival rate to queue i,\lambda_{i} , is proportional to N , the number of customers in the system, i.e., \lambda_{i} = N\alpha_{i} , then we a) compute the value of N which saturates the system and b) predict which queue will first become saturated as N is increased towards this value.

Abstract: We introduce a priority queue-discipline that is designed for loss systems (i.e., those with no waiting positions) in which the priority class of a customer can be determined only when the customer starts service. When the arrival processes are Poisson and the service times are exponentially distributed, we obtain a simple formula for the steady-state probability that an arrival of a given class will be served.

Abstract: An algorithm is presented to determine time-dependent as well as several stationary queue length characteristics for single-server queues, in which the service transaction can consist of two components: the normal service time and the post-service time, In particular, a component wise non-preemptive priority discipline is considered, where the customers waiting for receiving their normal service time are preferred in face of the customers waiting for receiving their post-service time. The stationary characteristics of the total number of customers are obtained by solving a system of relationships between them where only one fixed stationary characteristic must be calculated explicitly.

Abstract: Consider a multi-priority, nonpreemptive, N-server Poisson arrival queueing system. Service times are negative exponential. In order to save available servers for higher priority customers, arriving customers of each lower priority are deliberately queued whenever the number of servers busy equals or exceeds a given priority-dependent cutoff number. A queued priority i customer enters service the instant there are fewer than the respective cutoff number of servers busy and all higher priority queues are empty. The principal result is the priority i waiting time mean, second moment, and distribution (in transforms). The analysis is extended to systems in which any subset of priority levels may overflow to some other system, rather than join infinite capacity queues. The paper concludes with illustrative computational results.

Abstract: In this article the control of entry of customers to a queuing system with s servers is considered. It is assumed that the arrivals form a nonstationary Poisson process with a periodic rate. The service times are assumed to be exponentially distributed with a parameter independent of time. The cost structure considered is the same as that of Naor. It is demonstrated numerically that, like the stationary cases, the average expected benefit of customers per unit of time is a unimodal function of the critical point. And, also, the social critical point is smaller than the individual critical point. These suggest the use of a search technique for finding the social critical point. The results show successful application of the discrete version of the Fibonacci search.

Abstract: It is analytically difficult to derive the probability distribution function of waiting (or delay) time at the second or third queue in series of tandem queues. This paper presents a method by which approximation is done through a quasi‐isomorphic system which resembles the second queue in respect of one output, viz delay time. Through extensive simulation experiments these isomorphs have been derived. The procedure of getting a simple system to represent a part of a complex system is practised in cybernetics; this approach appears to have potentiality in studying intractable problems in communications and industrial management.