Abstract: We prove strong approximations for multiple channel queues in heavy traffic. Strong approximations are given for the waiting time and queue length processes, and for embedded sequences associated with the length process.

Abstract: The transactional data of a queueing system are the recorded times of service commencement and service completion for each customer served. With increasing use of computers to aid or even perform service one often has machine readable transactional data, but virtually no information about the queue itself. In this paper we propose a way to deduce the queueing behavior of Poisson arrival queueing systems from only the transactional data and the Poisson assumption. For each congestion period in which queues may form in front of a single or multiple servers, the key quantities obtained are mean wait in queue, time-dependent mean number in queue, and probability distribution of the number in queue observed by a randomly arriving customer. The methodology builds on arguments of order statistics and usually requires a computer to evaluate a recursive function. The results are exact for a homogeneous Poisson arrival process with unknown parameter and approximately correct for a slowly time varying Poisson process.

Abstract: In an ATM network, it can be necessary to protect some cells against rejection when entering finite-capacity buffers. “Space priority” is an access mechanism intended to provide such a protection by allowing them to take the place of less important cells in case of congestion. We study an M/G/1 queue using this operating mode and we compute loss probabilities for both flows. The model is then compared with the usual finite capacity queue in order to qualify space priority: reduction in buffer size, and increase in the admissible load for a given Grade of Service.

Abstract: The performance of an asynchronous transfer mode (ATM) network subject to admission control and traffic smoothing is analyzed. Basically, an ATM switch is modeled as a discrete-time single-server queuing system in which a new call joins existing calls. Cell arrivals from a new call are assumed to follow a general distribution. It is also assumed that aggregated arrivals of cells from existing calls form batch arrivals with a general batch size distribution and a geometric distribution of the interarrival times between batches. Both finite- and infinite-buffer cases are considered. An exact analysis yields the waiting time distribution and cell loss probability for a new call and for existing calls. Numerical examples are given to show how the network performance depends on the statistics of a new call (burstiness, time that a call stays in an active or inactive state, etc.) and to demonstrate the effectiveness of admission control and traffic smoothing. >

Abstract: We consider a tandem queueing system with m stages and finite intermediate buffer storage spaces. Each stage has a single server and the service times are independent and exponentially distributed. There is an unlimited supply of customers in front of the first stage. For this system we show that the number of customers departing from each of the m stages during the time interval [0, t] for any t ≧ 0 is strongly stochastically increasing and concave in the buffer storage capacities. Consequently the throughput of this tandem queueing system is an increasing and concave function of the buffer storage capacities. We establish this result using a sample path recursion for the departure processes from the m stages of the tandem queueing system, that may be of independent interest. The concavity of the throughput is used along with the reversibility property of tandem queues to obtain the optimal buffer space allocation that maximizes the throughput for a three-stage tandem queue.

Abstract: A packet communication system in accordance with the present invention wherein, when the system receives packets each made up of a predetermined until data from a plurality of terminals, these packets are arranged to once form a packet queue, the packets in the packet queue are sequentially and selectively transmitted, and the selection of one of the packets of the packet queue to be immediately transmitted is determined through simple operation, whereby high speed processing can be realized and discardable packets in the packet queue can be selectively discarded with high freedom.

Abstract: The queuing behavior of many communication systems is well modeled by a queuing system in which time is slotted and in which the number of entities arriving during a slot is dependent upon the state of a discrete-time, discrete-state Markov chain. The probability generating function is presented for joint and marginal buffer occupancy distributions of statistical time-division multiplexing systems in this class. A simple technique is discussed for obtaining moments of the queue length distribution. In addition, a discussion is presented of inversion of the probability generating function. Numerical results, including queue length distributions for some special cases, are presented. >

Abstract: The problem of assigning customers to one of several parallel queues so as to minimize the average time spent in the system (sojourn time) is studied as a Markov decision process. It is shown how the approach developed by K.R. Krishman and T.J. Ott (Proc. 25th IEEE Conf. Decision Contr. Dec. 1986, p.2124-8) to investigate state-dependent routing of voice traffic for blocking minimization can also be used for sojourn minimization for data traffic. For queues in parallel, this approach produces a rule, called the 'separable' rule, which is a generalization of the 'join the shortest queue' rule to the case of dissimilar queues, reducing to the shortest queue rule when the queues are all alike. Numerical results show that in cases where the queues are dissimilar in both the service rates and numbers of their servers, the separable rule is strikingly superior to the shortest queue rule; if the dissimilarities are limited to differences in the service rates, the separable rule practically always is better than the shortest queue rule; if the dissimilarities consist only of the numbers of servers being different, then the shortest queue rule does better than the separable rule in most instances. >

Abstract: This expository paper deals with the right tail behaviour of a class of Poisson mixtures. An Abelian-type result is obtained using basic theory of regular variation. Applications to compound distributions in insurance risk theory and queue length distributions under various queue disciplines in the case of Poisson arrivals are then discussed.

Abstract: A method for scheduling processes for execution in a computer system organizes the processes into run queues in accordance with the respective secrecy classes of the processes. A CPU time slot is assigned to each run queue. If all processes in a run queue give up the CPU before the expiration of the run queue's assigned time slot, the leftover time is given to a run queue whose secrecy class dominates that of the previous run queue. Covert-channel countermeasures are not taken in between two run queues if the secrecy class of the second run queue dominates the secrecy class of the first run queue.

Abstract: A processor-sharing queueing system is considered that can accommodate a finite number K of customers. In a processor-shared queue, every customer gets an equal fraction of the server (processor). The main quantity of interest in such a system is a customer’s response time (time spent in system) conditioned on that customer’s total required service and the number of other customers present at the arrival time. Using singular perturbation methods, we construct asymptotic expansions for the first two moments of the conditional response time for systems where the capacity K is large.

Abstract: The control of congestion in asynchronous transfer mode (ATM)-based networks is an important and complex subject that must be properly addressed in order to permit efficient use of network capacity while providing good quality of service to all network users. This congestion control problem is characterized here, and the performance-related aspects of some key congestion control features are modelled. Congestion controls for a broadband network will include features for admission control, buffer and queue management, traffic enforcement and reactive control. This paper identifies the leading alternatives for each of these congestion control features, presents an approach for comparing these alternatives based on the relative efficiencies achievable with each, and suggests one reasonable set of congestion control features. Our approch for comparing congestion control alternatives is based on a suitable model for the congestion-related functions of an ATM-based network, togther with a characterization of the traffic loads imposed by various broadband services.

Abstract: In this paper we present a queue that has two classes of customers: readers and writers. Readers access the resource concurrently and writers access the resource serially. The queue discipline is FCFS: readers must wait until all writers that arrived earlier have completed service, and vice versa. The approximation can predict both the expected waiting times for readers and writers and the capacity of the queue. The queue can be used for the analysis of operating system and software resources that can be accessed both serially and concurrently, such as shared files. We have used the queue to analyze the performance of concurrent B-tree algorithms.

Abstract: The architecture and performance of fixed-node virtual channel (VC) routing in asynchronous transfer mode (ATM) networks is studied. In fixed-node routing, only the nodes are specified, and any of the available parallel links between nodes may be used. Applying the fixed-node routing architecture in ATM networks has the advantages of more efficient use of network resources, better availability/reliability and performance, and the ability to support superrate services. The sequencing problem associated with this approach in conventional packet-switched networks can be easily solved in the ATM environment. An analysis is presented of the performance of this routing architecture for an internally nonblocking ATM switch with partially shared output buffers based on a discrete-time D/sup (A)//D/c/B queuing system for general input traffic. A D/sub 1/+ . . . +D/sub N//D/c/B queuing system is used for deterministic traffic. It is shown that the fixed-node routing architecture yields better performance in terms of delay, loss probability, channel utilization, and switch throughput than its fixed-path counterpart. >

Abstract: This paper investigates a single-server priority queueing system with batch arrivals where an arriving batch is composed of multi-class customers. The main motivation for studying this type of priority queue is its potential applicability to communication switching systems. Preemptive resume and nonpreemp­ tive (head-of-the-line) rules are considered. The queue length and waiting time distributions are obtained via the supplementary variable technique and delay cycle analysis. The conservation law approach is applied to find the mean delay formulas.

Abstract: This paper analyzes a queueing system consisting of a single server which dispenses service to jobs of K � 1 priority classes. Jobs are assumed to arrive to the queue according to a Poisson point process with a class dependent rate and to have class dependent service demands that are generally distributed. A linear priority function of the time spent in the system is specified for each job class and is used to schedule jobs. Specifically, the server, when available for service, nonpreemptively selects the job having the highest priority value to be the next job scheduled. Previous work in analyzing a system of this type has concentrated on providing bounds on the expected class response time. We extend these results by providing a closed form expression for the mean class response time and an expression for the ratio of expected response times in the limiting case of heavy traffic. We also provide a closed form expression for the mean class response time under certain light load conditions.

Abstract: The problem of the optimal admission and routing of customers to a network of two infinite server queues in parallel is considered. The service times in the two queues are exponential with a common rate. The arrival process is Poisson. There is a nonnegative cost associated with rejecting a customer and a cost of holding a customer in each queue. This holding cost is a nondecreasing convex function of the number of customers in that queue and is different for each queue. It is shown that the optimal control policy has admission monotonicity and routing monotonicity properties. >

Abstract: We study a multi-server multi-queue system which is intended to model a local area network with slotted ring protocol. Two special cases of the model are analysed and the results are used to motivate an approach to approximate mean queue lengths in the general model.

Abstract: The customer response times in the egalitarian processor sharing queue are shown to be associated random variables under renewal inputs and general independent service times assumptions.

Abstract: The server visits N queues in an arbitrary manner. Each queue is visited for a random period of time whose duration is sampled in advance. At the end of a visit period, either all customers of the attended queue leave the system (variant I) or only customers that were present in the queue upon the arrival of the server leave the system (variant II). A scheduling policy is a rule that selects the next queue to be visited by the server. When the controller has no information on the state of the system, it is shown, under homogeneous arrival assumptions, that a cyclic policy minimizes the expected number of customers in the system. When the controller knows the number of customers in each queue, it is shown that the so-called most-customers-first (MCF) policy minimizes, in the sense of strong stochastic ordering, the vector of the number of customers in each queue whose components are arranged in decreasing order. These results hold for variants I and II and are obtained under fairly weak statistical assumptions. This model has potential applications in videotex and time-division multiple-access systems. >

Abstract: The resequencing delay for a queueing system with multiple servers under threshold-type scheduling is analyzed. The general expressions for the average total delay, which is the sum of resequencing delay and queuing delay, are derived. The expressions are also applicable to the conventional M/M/n queuing system as the special case of zero-threshold policy. Next, the numerical calculation is carried out for a queuing system with three servers under a threshold-type schedule to consider the impact of the multiple thresholds on the average resequencing delay. It is found that the resequencing delay as well as the queuing delay for a queuing system with multiple servers of different service rates can be reduced under threshold-type scheduling by selecting the threshold values appropriately. Threshold-type scheduling is more effective in reducing the resequencing delay compared to the queuing delay, especially in the region of modest traffic intensity and as the difference in the service rates becomes larger. >

Abstract: There is provided a queue management system comprising a dispensing means (1) for dispensing to a customer a queue-position indication, a main display means (2) for displaying information in relation to the service position at the head of the queue, "slave" customer display units (3) and individual remote control units (4) and a master remote control unit (5). The queue-position indication on the display means (2) is remotely controllable. A processing unit may be provided to process data received from the remote control units (4, 5) and dispensing means (2) to enable the system to be monitored.

Abstract: The SCHEDULE parallel programming package has been modified so that many more total processes may be spawned as long as the number of currently active processes satisfy the former limits of the package rather than the cumulative total number. This has been accomplished principally by changing the queueing system for both the job parameter queue and the ready jobs queue. The original linear queues are converted to circular queues, in that finished places in the queues are reused for new jobs and that the physical end of the queue is logically connected to the physical beginning of the queue. Two additional features facilitate the change in queues. The first is the implementation of a third queue, a free list, which keeps a list of the currently free slots on the job parameter queue. The second new feature is the use of SCHEDULE generated job tags rather than user-generated job tags within the package. The user program now gets a job tag number from SCHEDULE with a subroutine call. Another improvement permits the iteration of dependency graphs, with minimal restoration of dependency data. This improvement facilitates the application of the SCHEDULE package to iterations and time-stepping problems, by saving and reusing the iterated part of the dependency graph. This feature can result in a significant reduction in the number of newly spawned processes that would otherwise be needed for iterations.

Abstract: An interleaved output queue is used as a high performance interface on a system bus for transferring information from a CPU to main memory. The queue is loaded on its input side with information that is bound for transmission from the CPU's cache to main memory. The queue itself is logically divided into those queue entry addresses which are either odd or even. On its output side, the queue is unloaded by dual sets of unload circuitry, each of which accesses the information stored in either the odd or even queue entry addresses. Other select circuitry will alternate the transmission of information out of the two sets of unload circuitry to main memory. Each set of unload circuitry receives error information back from main memory during the time that the other unload circuitry is issuing a transaction. As a result, each set of unload circuitry is thereby informed whether its own previous transaction was error free, in which case it will transmit the information contained in its next queue entry address when it next issues a transaction, or whether its previous transaction was not error free, in which case it will next have to resend the same information sent during the previous transaction. Consequently, transactions issued from the queue can proceed in an immediately successive sequence without waiting for the processing of error information from the immediately preceding transaction yet the queue can still recover form errors during high performance operation.

Abstract: Recent work in queueing theory has provided a means by which queue lengths can be estimated based solely on information about service completions. The work yields algorithms that permit the estimation of invisible or disperse queues which would be difficult to measure directly. These algorithms may be applied to resources in communications networks at which difficult-to-measure queues exist. The following paper presents an algorithm for queue estimation and measures its accuracy on transmission data taken from an ethernet environment. Results show the algorithm to be fairly accurate despite its simplifying assumption that the arrival process of the data packets is Poisson; for about 2/3 of the queues analyzed, the ratio of the root mean square difference between the real queue and the estimated queue to the average real queue is less than 1/2.

Abstract: This paper is concerned with single server queues having LCFS service discipline. We give a condition to hold an invariance relation between time and customer average queue length distributions in the queues. The relation is a generalization of that in an ordinary GI/M/1 queue. We compare the queue length distributions for different single server queues with finite waiting space under the same arrival process and service requirement distribution of customer and derive invariance relations among them.