Showing papers on "Server published in 1978"
TL;DR: In this article, the authors consider a queuing system with several identical servers, each with its own queue, and assign the arriving customers so as to maximize the number of customers which complete their service by a certain time.
Abstract: We consider a queuing system with several identical servers, each with its own queue. Identical customers arrive according to some stochastic process and as each customer arrives it must be assigned to some server's queue. No jockeying amongst the queues is allowed. We are interested in assigning the arriving customers so as to maximize the number of customers which complete their service by a certain time. If each customer's service time is a random variable with a non-decreasing hazard rate then the strategy which does this is one which assigns each arrival to the shortest queue.
332 citations
TL;DR: Before designing a computer program for allocating police patrol cars by time and geography, a review was undertaken of previously existing programs of this type and none of the programs had achieved general acceptance because each had virtues and inadequacies not present in the others.
Abstract: Before designing a computer program for allocating police patrol cars by time and geography, a review was undertaken of previously existing programs of this type. Nearly all of the programs calculated queuing statistics for the collection of patrol cars by assuming a steady-state system with calls for service arriving within priority levels according to Poisson processes and having independent, identical, exponentially distributed service times. Unavailabilities of patrol cars for reasons other than calls for service were handled in the models either by artificially increasing the arrival rate of calls or by assuming that the number of servers is smaller than the number of patrol cars. Some programs calculated additional performance measures such as travel times and preventive patrol frequencies. All the programs had the capabilities to describe performance statistics for an allocation proposed by the user, but they differed in their capabilities to prescribe desirable allocations. None of the programs had achieved general acceptance because each had virtues and inadequacies not present in the others.
73 citations
TL;DR: This paper makes an attempt to approximate stochastically the behaviour of a general many server queue by using single server queues as stochastic bounds, and proposes three alternative ways of constructing approximating singleserver queues.
Abstract: Obtaining time dependent results for many server queues is, under general structural assumptions, a hard problem. This paper makes an attempt to approximate stochastically the behaviour of a general many server queue by using single server queues as stochastic bounds. We propose three alternative ways of constructing approximating single server queues. The first technique utilizes special classes of service time distributions new better than used, new worse than used, the second is via dividing the service times by the number of servers, and the third is based on a grouping idea of the customers. The first and third techniques yield in fact two bounding queues each, one of which is faster and one slower than the original s-server queue.
45 citations
TL;DR: An exponential queuing system consisting of several removable servers in which the arrival rate depends on the current system state is considered, and conditions that ensure that the number of servers in operation is a non-decreasing function of thenumber of customers in the system are presented.
Abstract: We consider an exponential queuing system consisting of several removable servers in which the arrival rate depends on the current system state. Costs are incurred at a rate that depends on both the number of customers present and the number of servers in operation. We present conditions that ensure that the number of servers in operation is a non-decreasing function of the number of customers in the system.
27 citations
TL;DR: A Markov process model for computing the operating characteristics of the radio-dispatched fleet operating under a policy that dispatches the closest available unit to each call for service (implying use of a perfect resolution AVL system), and a realistic nine-unit police example that indicates the general ways in which AVL dispatching improves (and degrades) system performance.
22 citations
TL;DR: In this article, the authors make an attempt to approximate stochastically the behaviour of a general many server queue by using single server queues as stochastic bounds, and propose three alternative ways of constructing approximating single server queues.
Abstract: Obtaining time dependent results for many server queues is, under general structural assumptions, a hard problem. This paper makes an attempt to approximate stochastically the behaviour of a general many server queue by using single server queues as stochastic bounds. We propose three alternative ways of constructing approximating single server queues. The first technique utilizes special classes of service time distributions new better than used, new worse than used, the second is via dividing the service times by the number of servers, and the third is based on a grouping idea of the customers. The first and third techniques yield in fact two bounding queues each, one of which is faster and one slower than the original s-server queue.
21 citations
TL;DR: In this paper, a cyclic queueing network with two servers and a finite number of customers is studied, where the service times for server 1 form an EARMA(1,1) process, which is a sequence of positively correlated exponential random variables; the process in general is not Markovian.
Abstract: : A cyclic queueing network with two servers and a finite number of customers is studied. The service times for server 1 form an EARMA(1,1) process (exponential mixed autoregressive moving average process both of order 1) which is a sequence of positively correlated exponential random variables; the process in general is not Markovian. The service times for the other server are independent with a common exponential distribution. Limiting results for the number of customers in queue and the virtual waiting time at server 1 are obtained. Comparisons are made with the case of independent exponential service times for server 1.
16 citations
TL;DR: Although this problem arose in the study of data interpolation in STDM and TASI systems, the queueing model developed is quite general and may be useful for other industrial applications.
13 citations
01 Jan 1978
TL;DR: The George grant in process essays and conversations as discussed by the authors is available in the digital library and an online access to it is set as public so you can download it instantly, and it is universally compatible with any devices to read.
Abstract: george grant in process essays and conversations is available in our digital library an online access to it is set as public so you can download it instantly. Our book servers spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the george grant in process essays and conversations is universally compatible with any devices to read.
8 citations
Posted Content•
TL;DR: In this paper, a non-dynamic system is used to estimate the probability of a customer being blocked in a network of servers, known as a grading in telecommunication engineering, and the resulting variance is derived using the renewal or regenerative property of such systems.
Abstract: A network of servers, known as a grading in telecommunication engineering, is simulated in order to estimate the probability of a customer being “blocked”: all servers busy. Since blocking is a very rare event (1‰ to 5% chance), importance sampling was considered for reduction of the simulation variance. The basic idea of importance sampling is first explained by means of a non-dynamic system. For dynamic systems a method was proposed by Bayes in 1970, which is related to the “virtual measures” published by Carter and Ignall in 1975. For simple queuing systems, we derive the resulting variance, using the renewal or regenerative property of such systems. For our practical “grading” system several alternative importance regions are investigated. For practical reasons we choose to start an importance region immediately after a call gets blocked (not a renewal state). The analysis and simulation experiments for the resulting estimator yielded the estimated optimal length of the importance region and the optimal number of replications of the region. Unfortunately, a net increase in variance resulted.
3 citations
IBM1
TL;DR: In this paper, a system of N unlimited queues and N time-discrete servers in series, where requests which have been generated according to the i-th process leave the system after they have received serivice by servers 1, 2,...,i.
Abstract: A system ofN unlimited queues andN time-discrete servers in series, is investigated. The input consists ofN stochastic processes where requests which have been generated according to thei-th process leave the system after they have received serivice by servers 1, 2, ...,i. The holding-time distributions can be calculated by means of an equivalence theorem which holds under certain conditions for the service times.
TL;DR: In this article, the authors considered a two server congestion system where the reward received depends on the match between server and customer, and the policy that maximizes the long-run expected reward over an infinite horizon was shown to depend on a single critical number.
Abstract: We consider a two server congestion system which is heterogeneous in the sense that the reward received depends on the match between server and customer. In particular, if a type s customer (s = 1, 2, 3, …) is assigned to server i (i = 1, 2) a reward Rst is earned. Service time is assumed to depend only on customer type. Upon arrival a customer must be assigned to a server, (if one is available) with all customers who find both servers occupied being turned away. The policy that maximizes the long-run expected reward earned over an infinite horizon is shown to depend on a single critical number. Applications to the deployment of fire engines and assignment of patients to coronary care units are briefly discussed.
Book•
01 Jan 1978
TL;DR: The max beckmanns zeichnerisches werk 1903 1925 is universally compatible with any devices to read and an online access to it is set as public so you can download it instantly.
Abstract: max beckmanns zeichnerisches werk 1903 1925 is available in our book collection an online access to it is set as public so you can download it instantly. Our book servers saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the max beckmanns zeichnerisches werk 1903 1925 is universally compatible with any devices to read.
TL;DR: In this paper, a measure of ineffectiveness of a pool of independent service facilities is defined and it is shown to be rather insensitive to changes in the service-time distribution for queues with a Poisson input, assuming equal mean service rates of the servers.
Abstract: A measure of ineffectiveness I of a pool of independent service facilities is defined and it is shown to be rather insensitive to changes in the service-time distribution for queues with a Poisson input, assuming equal mean service rates of the servers. This result reduces consideration to the simple case of exponentially distributed service times and in this case (i) I can be computed using well-known formulae and (ii) it is possible to construct a simple upper bound for I.