Abstract: Many computer algorithms have embedded in them a subalgorithm called a priority queue which produces on demand an element of extreme priority among elements in the queue. Queues on unrestricted priority domains have a running time of Θ(nlogn) for sequences ofn queue operations. We describe a simple priority queue over the priority domain {1,⋯,N} in which initialization, insertion, and deletion takeO(loglogD) time, whereD is the difference between the next lowest and next highest priority elements in the queue. In the case of initialization,D=Θ(N). Finding a least element, greatest element, and the neighbor in priority order of some specified element take constant time. We also consider dynamic space allocation for the data structures used. Space can be allocated in blocks of size Θ(N 1/p ), for small integerp.

Abstract: A customer queue control system for an establishment having a plurality of customer service stations utilizes a main queue and a plurality of local queues, and includes a detector to detect the presence of a customer at the head of the main queue, keys at each service station to signify the status of that station, a voice message device to direct a customer at the head of the main queue to a local queue selected to provide the probable minimum waiting time, and a data processing system for controlling the voice message device in accordance with the presence of a customer in the main queue, the number of customers in each local queue, the status of each local queue, and the probable service delay time per customer in each local queue.

Abstract: The exponential open queue network model studied here consists of n symmetrical queues in parallel served by independent first-level servers in tandem with a second-level server. Blocking of the flow of units through a first-level server occurs each time the server completes a service. The server remains blocked until its blocking unit completes its service at the second-level server. An approximate expression of the probability distribution of the number of blocked first-level servers conditioned upon a service completion of a first-level server is obtained. This expression compares well with simulation data. Based on this distribution, an approximate expression of the queue-length probability distribution is derived assuming a processor-sharing type of service. The exact condition for stability of the queue network is also derived. Some potential applications are discussed, and a quantitative evaluation of the model is given through a case study.

Abstract: A data communications system to provide for the dynamic modification of a queue of documents arranged sequentially for transmission. An operator interacts with the send queue by making the send queue selection from a menu of communication request tasks on a display. Selection of the addition to the send queue option invokes a routine to add a send job. Operator selection of the display send queue option invokes a routine to display the send queue in the display for review of the current send queue and its status. A delete send job option invokes a routine to allow the operator to delete any job from the send queue except the one currently being sent. The select next send job option invokes a routine to allow the operator to start or restart the sending process from any point within the send queue.

Abstract: OF THE DISCLOSURE A memory controller controls the operation of a number of memory module units and includes a number of queues which couple to the module units. Each queue includes an address queue register, a control queue register and a data queue register. Each address queue register has tristate control for independent operation. Control circuits which couple to the queue address, control and data registers assign memory cycles between queues on an alternate basis when the queue control registers store requests which are being processed. This enables the interleaving of memory requests which elimi-nates processing delays particularly in cases where such requests involve multiword transfers over successive memo-ry cycles of operation.

Abstract: A tandem queueing system with constant slotted service times and threshold control is modeled and analyzed in this paper. The input to the first queue is controlled by the buffer occupancy of the second queue. When the second queue has more than No customers, the input to the first queue will be rejected. The input to the second queue consists of the output from the first queue and an external input which is assumed to be Poisson distributed. The behavior of such a queueing system is analyzed and portrayed in graphs. The threshold control rejects input traffic to the first queue and avoids congestion at the second queue. As a result, the delay for an arrival to be serviced by both of the queues is much lower than the case without threshold control. As No increases, the system behavior approaches the case of the system without threshold control. Such a queueing model is motivated by congestion control in a computer network. An example is given to illustrate the applications of gateway flow control in internet- working.

Abstract: — The queue network model studied in this paper consists of two symmetrical queues in parallel served by a first level of servers and linked to a second-level server with no intermediate waitingroom. Bloçking of the flow of units through a firste el server occurs each time the server complètes a service, The server remains blocked and it can not serve any other units until the bloçking unit complètes Us service at the second-level ̂ server. An approximate expression of the generating function, g (z), of the queue-length distribution is obtained. The queue-length distribution is then derived by inverting g (z). The results obtained compare very well with simulation data, The exact condition for stability of the queue network is also derived.

Abstract: A memory controller 200 controls the operation of a number of memory module units A to D, 210 and includes a number of queues 207-80 which couple to the module units. Each queue includes an address queue register, a control queue register and a data queue register. Each address queue register has tristate control for independent operation. Control circuits 215 which couple to the queue address, control and data registers assign memory cycles between queues on an alternate basis when the queue control registers store requests which are being processed. This enables the interleaving of memory requests which eliminates processing delays particularly in cases where such requests involve multiword transfers over successive memory cycles of operation.

Abstract: A Message Channel is defined as a tandem connection of single server queues in which the successive service times experienced by any particular customer are scaled versions of the same random variable, and thus it serves as a model for sparsely connected store-and-forward data communications networks (or network segments) where messages typically preserve their lengths as they traverse the system . A particular instance of sucha nonstandard queueing model is analyzed in this paper. The system consists of two single server queues in tandem subject tao Poisson arrival process (at the first queue) and providing service according to scaled versions of a sequence of two-level, discrete random variables. A set of recursive equations that can be used to solve the model for any given scaling factor at the second queue (normalized with respect to the first queue service) is explicitly derived. In addition, complete solutions are displayed for several cases of interest, and the equilibrium mean cumulative waiting times for these instances are compared as a method of indicating the impact of the scaling factor on the operation of the system. The extension of several results to systems with more general service time processes is discussed.

Abstract: A new approach is proposed to model heavy traffic queuing behaviour by stochasticizing in various ways the arrival and service rates so as to incorporate the random effect of the environment. This approach yields for the queue size a differential equation with stochastic parameters. The corresponding Fokker-Planck equation for the probability density function of the queue size is employed to analyse the queuing system. In this framework we consider the arrival and service rates to be subject to gaussian, white-noise perturbations and obtain the probability density function of the queue size and the distribution of the busy period. The study is generalized by considering the effect of coloured-noise perturbations in these rates. The effect of the white-noise perturbations on the state-dependent service rate is also investigated.

Abstract: One of the most common data structures in programs is the queue, which is used frequently as a buffer between processing elements.

Abstract: Models for time-sharing computer systems are presented. The models are of the repairman type and involve more than one type of customer demanding service from a single server queue. The models studied do not admit a product form stationary distribution, thus approximation methods designed to study the queue length processes are introduced. Of particular importance is the introduction of an approximation method which allows for the queue discipline to be varied parametrically. The associated diffusion approximation allows one to study system performance as a function of queue discipline.

Abstract: This paper is concerned with a system of two queues in tandem where each queue has a single exponential server. The rates. of the servers may differ. The first queue has an infinite waiting room, whereas the second queue has no waiting room. Initially the system is empty. Customers enter the first queue according to a renewal input process, and then pass through the second queue. We are concerned with the sojourn time of a customer in the system. We show that the queues are interchange­ able, in the sense that the order of queues does not affect the sojourn and delay distributions.

Abstract: This paper is concerned with the following two-stage tandem queueing system (TQ for short). There are two service facilities (or servers for short) arranged in tandem. Each customer arriving at the system receives the service from the first server (server 1), and then the second (server 2), before leaving the system. The queue before the server 1 may be allowed to grow unlimitedly, whereas no queue before the server 2 is allowed. If the server 2 is busy, therefore, when a service is completed to a customer by the server 1, this customer stays at the first stage and blocks fur ther service until the server 2 becomes free. The service discipline is defined on FCFS basis. The n th customer C~ arrives at t ime T~ and has a service t ime Sk,~ by the server /c ( k = l , 2), and we define A~=Tn-T~_, for n = l , 2 , . . . , where T0=0. It is assumed tha t $1,~, S,.~, . . . , $2,,, $2,~., . . . , A, , A2, . . . are mutually independent, the S,.~'s are identically distributed random variables (r.v.'s) with distr ibution function (d.f.) G, ( k = l , 2), and A~'s are also identically dist r ibuted r.v. 's. For such a TQ, a notation GI/G1---~G~ is employed. For the GI[GL---*G~. queue, accurate analysis of the d.f . ' s of such characteristic quantities as the sojourn and delay times of a customer and the number of customers in the system is extremely difficult and even their expectations cannot be computed analytically, except for some special cases, e.g. in Suzuki [10], Avi-Itzhak and Yadin [1], Tumura and Ishikawa [11]. Therefore, bounds for these d.f . ' s and expectations are of value. Special interest lies in the bounds given by characteristics of other queueing systems which are relatively analyzed easily. For usual GI] G/m queues there exist such useful bounds included in Brumelle [4], H. Stoyan and D. Stoyan [9] and Miyazawa [6]. From this viewpoint Sakasegawa and Yamazaki [7] tried to compare the GI/GI---~G~ queue with the following single server queueing system

Abstract: This study examines how customers joining a queuing system assess their waiting time in the system. Data obtained from an actual queuing system support the paradigm of Parkan and Warren [5] on the use of the observed number in the system in this assessment. It is concluded that customers overestimate mean service time but that this overestimation is not dependent on the number in the system.

Abstract: A system of two parallel queues is considered, where each customer must leave after service through a common gate G. It is assumed that service times at the two stations I and II are independent and identically distributed, and that exit service takes a fixed length of time. A I-customer may be served at station I only if the previous I-customer has completed exit service. Integral equations are formulated from which the distribution of the total service time may be obtained when the two queue sizes are infinite. These equations are solved for exponential and generalized erlangian service times. Extensions to the case of k parallel queues and to the case of Poisson arrivals and finite queue sizes are discussed briefly.

Abstract: SYNOPTIC ABSTRACTIn this paper we consider an M/G/1 queue with non-preemptive priority service discipline and N-control policy (of Heyman, Yadin and Naor). The Laplace-Stieltjes transforms of the waiting times are derived using properties of level crossings of regenerative processes and delayed busy cycles. The mean waiting times, the mean cost rate, and the optimal policy are also derived. Use of these results is illustrated through two numerical examples.

Abstract: A classical method of measunng the number of lobs m a trine-shared computer system ,s to collect statistics at the epochs of quantum completions. A computer system utilizing round-robin quantum allocations ~s modeled as a feedback queue with Poisson amvals and exponential service times, and the bias in the stausuc taken at the quantum compleuons is quant,fied. The difference botween this statistic and the true Ume-average system size is given for such a system including quanta and overhead.