Abstract: New results are obtained for the single server queue with Poisson arrivals and exponential service times. A closed form solution involving only finite sums is obtained for the probability that exactly i arrivals and j services occur over a time interval of length t in a queueing system that is idle at the beginning of the interval. Since many applications of queueing theory involve queues which are emptied and restarted periodically and thus not susceptible to analysis using the well-known equilibrium results, there are many potential applications for results obtained. Some ways in which the results obtained may be applied are discussed.

Abstract: The first paper to introduce the concept of a cyclic queue appeared in the Operational Research Quarterly in 1954. The paper dealt with the 'flow' of aircraft engines from operation to maintenance to available for operation. In 1958, the first paper analyzing the cyclic queue model appeared in the same journal. This paper was application of queue theory to underground coal mining. In 1965 it was shown that stochastic queue networks can be treated analytically in the same manner as cyclic queues with a small adjustment in the auxiliary parameters. Since then cyclic queue models have been applied not only to the problems mentioned above but also to many other production and service industry problems: computer design and control, ship operations, production processes, communications flow, ingot movements in a steel mill, to name but a few. In order for this to be possible, extension and advances in theory have been required and these have come from many nations and many fields of endeavour. This paper traces the development of the theory of cyclic queues and queue networks from 1954 to the present.

Abstract: User actuates real time resource reallocation in a multi-tasking environment wherein the operating system builds a process queue against a resource and wherein a new task is interrupt invoked with the dispatcher allocating the resource to the next task in the queue, the queue switching being orthogonol to the dispatcher scheduling of processes.

Abstract: This paper studies the queue length distributions of a discrete time bulk server queue with time-inhomogenous compound Poisson input in which service is provided in time-inhomogenous batches and the interarrival times of the server have a general distribution. We assume that the service epochs form a renewal process. This sort of queue occurs during peak periods at intermediate bus stops, where passengers are waiting to catch a bus. In the queueing literature, this problem is known as a transportation type problem. The joint distribution of the number of customers waiting at any epoch and the remaining time before the next arrival of the server is obtained. The results are then extended to cover the case in which the waiting space is limited.

Abstract: A general method of analyzing the behavior in heavy traffic of queues with different impartial queue disciplines is described. There are many possible limiting waiting time distributions though all are mixtures of negative exponentials. The exponential distribution itself, however, shows a degree of robustness to departures from the “first come first served” discipline.

Abstract: We first consider a wide class of single-server queues with state dependent Markovian input including the finite capacity M/G/1 queue and the machine repair problem. We specify efficient and stable algorithms to compute the steady-state probabilities and the moments of the waiting time. Next we discuss the multi-server queue with Poisson input and general service times. We present for the steady-state probabilities good quality approximations to be computed from a stable recursive algorithm. As a by-product we obtain simple approximations for the delay probability and the moments of the waiting time. For the output process we derive tractable and good approximations for the moments of the interdeparture time. Also we discuss extensions to the finite capacity M/G/c queue and the machine repair problem with multiple repairmen having general repair times.

Abstract: Previous research on delay-dependent priority queues is generalized to the case of general independent service times and where the priority of classes of units is permitted to increase or decay linearly with time. An expression for expected class waiting time for such systems is provided.

Abstract: Consider a queueing system in which customers (or jobs) arrive to one of Q separate queues to await service from one of S identical servers (Figure 1). Once a job enters a queue it does not leave that queue until it has been selected for service. Any server can serve any job from any queue. A job selected for service cannot be preempted. In this paper we consider jobs to be in a single class; for the multiple class result see [AFSH81a]. We assume once a queue has been selected, job scheduling from that queue is fair. In particular, our results hold for first come first serve as well as random selection [SPIR79] and, for that matter, any fair nonpreemptive scheduling policy within a queue. We assume that arrivals to each queue follow a Poisson process with the mean arrival rate to queue q being lq. The S identical exponential servers are each processing work at a mean rate of m.This system is general enough to be adaptable for modeling many different applications. By choosing the policy employed for queue selection by the servers, we can model multiplexers, channels, remote job entry stations, certain types of communication processors embedded in communication networks, and sets of shared buses. In this paper we will use the latter application to discuss a realistic situation. The elements (“jobs”) in the queues are messages to be sent from modules connected to the shared bus of the system. The servers are the buses; their service times are equal to the message transmission times. The queues are in the interface modules connected to and sharing the buses.

Abstract: Customer queue control apparatus for an establishment having a plurality of service stations (40-50) utilizes a main queue and a plurality of local queues having not more than two members, at the individual service stations (40-50). A switch (66) detects the presence of a customer at the head of the main queue and keys (52) at the individual service stations (40-50) are utilized by the operators to signal that the station is open for business or that a customer has left the station after service. A synthesized voice message directs the customer to a local queue determined to have the expected minimum waiting time, dependent on the number of customers in each local queue, and the probable service time per customer in each local queue.

Abstract: In this paper we deal with a network of parallel queues. It consists of a switch and s server queues. Such a network we call a module; see Figure 1. Each queue of the module has unlimited waiting room. Queueing disciplines at queues of the network need not be the same and they belong to a broad class of so called work conserving normal (WCN) disciplines. The class of WCN disciplines was introduced by Rolski (1981a). In this paper we follow a definition given by Szekli (1981) which is recalled in Section 2. The sample history of a module is completely determined by a so-called generic sequence {T, S, X} = {(Ti, Si, Xi), i = 0,1,...} where Ti denotes the inter-arrival time between the i-th and (i+1)-st customer in the module, Si denotes the service time of the i-th customer, and Xi denotes the queue to which the i-th customer is routed. We assume that the module is initially empty. The triple (Ti, Si, Xi) is called the basic datum associated to the i-th customer to arrive at the module.

Abstract: We analyze a traffic overflow system that consists of two groups of trunks, with waiting spaces for each group, and some overflow capability from the primary to the secondary group. We consider the case in which the number of waiting spaces in the primary queue is large compared to the corresponding number in the secondary queue and to the number of trunks in the secondary group. The case of an infinite number of waiting spaces in the primary queue is also allowed. We contrast the approach presented with some previous approaches that are suitable when the number of waiting spaces in the primary queue is not comparatively large. As with previous approaches, the aim is to reduce the dimensions of the system of equations to be solved in order to calculate various steady-state quantities of interest. Our results include expressions for the loss probabilities, the probability of overflow from the primary to the secondary group, and the average waiting times in the queues. We also obtain the stability condition under which the results are valid when the number of waiting spaces in the primary queue is infinite.

Abstract: Many queues are characterized by predictable periodic fluctuations as well as by random fluctuations. Queues that arise at copiers or duplicators usually involve such predictable fluctuations in work-load arrival. This note describes a series of approximations that have been combined into a simple inexpensive computer program. This program is being routinely used by the Xerox Corporation to approximate the average turnaround time at nonstationary single-server queues with nonexponential service time distributions.

Abstract: We consider the problem of optimal control of a queueing system consisting of a common queue feeding two servers of different rates. Arrivals to this system form a Poisson process and the service times are exponentially distributed. Whenever a server is idle a decision has to be made on whether to feed a customer from the queue to the idle server. The cost criterion which we desire to minimize is the average number of customers in the system or equivalently, the mean waiting time of the customers. It is shown that the optimal policy is of threshold type, i.e. the slower server should be fed a customer only when the queue length exceeds a certain threshold value.

Abstract: PURPOSE:To assure the continuity of the process, by collecting the data to a queuing system and then copying them every time the process of the on-line system comes to a checking point CONSTITUTION:When the execution of a process 301 is over, the state of the own memory state concerning the process 301 is collected to a queuing system and then copied Then a checking point 1 is written into the own and queuing systems respectively After this, a process 302 is executed and then the state of the own memory state concerning the process 302 is collected to the queuing system and copied Then a checking point 2 is written into checking point storage tables 305 and 306 of the own and queuing systems respectively When processing is carried out in such a way, for example, if an on-line system has a breakdown under execution of the process 302, the queuing system can be started again at and after the process 302 since the results of processes up to the process 301 are copied at the queuing system by 401

Abstract: A simulation program is presented which predicts daily and seasonal deer (Odocoileus spp.) harvest based on a queuing model of hunter-deer interactions. Each day of the hunting season is simulated as a discrete-time system with the time increment the inter-arrival time between deer sightings. The hunter acts as a single server with a maximum queue length of 1 deer. The deer entering the queue for service (i.e., shot at) is the transaction that passes through the system. Various validation analyses showed that the model accurately predicts the daily and seasonal harvest. Sensitivity analysis demonstrated that the model predictions of deer harvest are stable relative to estimates of the number of deer at the start of the season and the daily number of hunters. With the model, the game manager can examine the effect of differing daily hunting pressures and bag limitations on deer harvest. The model can be adapted for different habitat types and other game species and can be used in conjunction with a population dynamics model. J. WILDL. MANAGE. 46(2):325-332 The white-tailed deer (Odocoileus virginianus) is one of the most important game animals of the United States (Halls 1978) and receives both intensive and extensive management. Field testing each possible management alternative is prohibitive in terms of time and money, political risks, and potentially undesirable effects on deer populations. A less costly technique, that lets the manager examine several different management plans and select that best suited for his needs at low cost and risk, is computer simulation (Hayne 1969). A number of deer management models have been developed. A gaming simulation of land use by Walters and Bunnell (1971) harvested big game at a predetermined rate. The primary goal of their model was to increase farm production and not big game harvest. Harvesting deer at a predetermined rate has been used in other simulation studies (e.g., Davis 1967, Brennan et al. 1970, Gross 1970). Models of this type tend to be unrealistic and difficult for the game manager to use in examining the effect of various hunting season regulations. Other deer management models have been based on energy flow or metabolism (e.g., Lomnicki 1972, Rayburn 1972, Walls 1974, Medin and Anderson 1979). The data required for such models are considerable and are costly in time and money to obtain. The actual harvest strategies in such models are predetermined by the game manager (e.g., Walls 1974). Regulations governing the number of hunters, length of the season, bag limit, and age and sex composition of the bag are important in the process of deciding strategies for managing a deer population. All major alternatives for different types of seasons and other restrictions must be examined to arrive at a harvest level that maximizes benefits and reduces adverse reactions (Mechler 1970). Queuing or waiting line models de1 From a dissertation submitted by Jacobs to the Graduate Faculty of Frostburg State College in partial fulfillment of the requirements for the degree of Master of Science. Contribution 1203-AEL, Center for Environmental and Estuarine Studies, University of Maryland. 2 Present address: Chesapeake Biological Laboratory, University of Maryland-Center for Environmental and Estuarine Studies, Box 38, Solomons, MD 20688. J. Wildl. Manage. 46(2):1982 325 This content downloaded from 207.46.13.184 on Wed, 19 Oct 2016 04:34:21 UTC All use subject to http://about.jstor.org/terms 326 DEER HARVEST QUEUING MODEL] Jacobs and Dixon scribe the movement of objects in a queue through a service mechanism such as customers waiting in a check-out line at a grocery store. A queuing system can be described by its input or arrival process, its queue discipline and its service mechanism. The arrival process usually is described by a probability distribution of time between successive arrivals. The queue discipline describes the order in which individuals in the queue are served. The service mechanism determines the time required to be served and the number of individuals that can be served at 1 time. Further description of queuing models can be reviewed in texts on operations research (e.g., Wagner 1975). There have been few queuing models applied to ecological systems. Curry and DeMichele (1977) used queuing theory to describe predatory-prey systems. However, no queuing models to date have been used to determine the effects that changes in hunting regulations would have on deer populations. The objective of this study was to develop a simulation of deer harvest based on a queuing model of hunter-deer interactions. Each day of the hunting season is simulated as a discrete-time system with the time increment the inter-arrival time between each hunter-deer interaction. The hunter acts as a single server with a maximum queue length of 1 deer; the deer entering the queue for service (i.e., shot at) is the transaction that passes through the system. The effect of varying the daily hunting pressure and bag limit (e.g., age, sex, and number) was examined with the model. We thank G. A. Feldhamer for answering questions concerning deer harvest and R. C. Weimer for staitistical assistance. The computer time was supported in full through the facilities of the Computer Science Center of the University of Maryland.