Abstract: The authors present and solve a discrete-time G/sup (X)//D/1-S queuing system with a finite queue size and batch arrivals with a general batch size distribution. The motivation for this model arises from performance modeling of a statistical multiplexer with synchronous transmission of fixed-size data units in synchronous time slots. The arrival process to the multiplexer, for example, may originate from a number of independent sources with packets of variable lengths. Hence, a packet arrival corresponds to an arrival of a batch of data units. Different performance measures such as percentage of packet loss and data-unit loss are considered under two different admission policies of packets into the queue. >

Abstract: Some sharp bounds and simple approximations are obtained for the Erlang delay formula and for the Erlang loss formula. One of the results is then used to get a simple analytical solution for the Server Allocation Problem.

Abstract: A data processor bus in which information is transferred between agents attached to the bus by issuing request packets that request data from an agent on the bus and reply packets that return data requested by a request packet. A control method mixes request-and-reply packets on the bus by determining the use of a next-bus cycle using arbitration, reply deferral, and specification lines and the state of a grant queue and a pipe queue in accordance with a specified protocol. A request is forced to take the next available bus cycle upon the condition that there is an agent identified in the great queue and the pipeline queue is not full. A reply packet is forced to take the next available bus cycle upon the condition that the pipeline queue is full. A reply packet is forced to take the next available bus cycle upon the condition that the grant queue is empty and the pipeline queue is not empty. Giving requests precedence over replies to allows the pipeline to be kept as full as possible. A replying agent assigned to the highest priority slot 1 in the pipeline queue is allowed to defer its own slot in the pipeline queue until a later time to thereby permit a transaction in Slot 2 of the pipeline queue to be completed before the one ahead of it.

Abstract: This paper discusses an approximation for single-class departure processes from multi-class queues: If the arrival rate of one class upon one visit to the queue is a small proportion of the total arrival rate there, then the departure process for that class from that visit should be nearly the same as the arrival process for that class for that visit. This can be regarded as a light-traffic approximation, but only the one class must be in light traffic; the overall traffic intensity of the queue need not be low. As a consequence, in a queueing network if the routing for one class is deterministic, and if the light-traffic condition applies at every queue this class visits, then the arrival and departure processes for this class at each visit to each queue should be nearly the same as its external arrival process. This approximation is explained in terms of different time scales, and is justified here by a limit theorem in a special case. There are important implications for parametric decomposition approximation techniques: the variability parameter partially characterizing the departure process at any visit to any queue of such a low-intensity class should be nearly the same as the variability parameter partially characterizing the arrival process for that class at that visit to that queue. The approximation principle in this form was recently proposed by G. Bitran and D. Tirupati while developing improved parametric-decomposition approximations for low-variability multi-class queueing networks with deterministic routing, which have important, applications in manufacturing. The approximation principle also has important implications for data networks showing how burstiness in originated traffic can pass through heavily shared network facilities where it has relatively little effect and then reappear at the destination.

Abstract: The authors examine the use of a group random-access protocol based on time windows for supporting time-constrained communication applications in a multiple-access network. First they formulate a policy for controlling protocol operation to minimize the percentage of messages with waiting times greater than some given bound. A semi-Markov decision model is then developed for protocol operation, and three of the four optimal control elements of this policy are determined. Although the semiMarkov decision model can also be used to obtain performance results, the procedure is to computationally expensive to be of practical use. Thus, an alternate performance model based on a queuing system with impatient customers is developed. Protocol performance under the optimal elements of the control policy shows significant improvements over cases in which the protocol is not controlled in this manner. Simulation results are presented to corroborate the analytic results. >

Abstract: Given a finite number of empty ./M/1 queues, let customers arrive according to an arbitrary arrival process and be served at each queue exactly once, in some fixed order. The process of departing customers from the network has the same law, whatever the order in which the queues are visited. This remarkable result, due to R. Weber [4], is given a simple probabilistic proof.

Abstract: We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: we study the long-run “state” behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptive-resume LIFO queue discipline is work-conserving, imply new representations for both “actual” and “virtual” delays in standard GI/G/1 queues with the FIFO (first-in-first-out) queue discipline. The arguments by which our results are obtained unveil the underlying structural “explanations” for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the well-known Benes's formula for the delay distribution in M/G/l. We also discuss how to extend our results to settings more general than GI/G/1.

Abstract: This paper considers a class of two discrete-time queues with infinite buffers that compete for a single server. Tasks requiring a deterministic amount of service time, arrive randomly to the queues and have to be served by the server. One of the queues has priority over the other in the sense that it always attempts to get the server, while the other queue attempts only randomly according to a rule that depends on how long the task at the head of the queue has been waiting in that position. The class considered is characterized by the fact that if both queues compete and attempt to get the server simultaneously, then they both fail and the server remains idle for a deterministic amount of time. For this class we derive the steady-state joint generating function of the state probabilities. The queueing system considered exhibits interesting behavior, as we demonstrate by an example.

Abstract: Consider a tandem queue model with a single server who can switch instantaneously from one queue to another. Customers arrive according to a Poisson process with rate λ . The amount of service required by each customer at the ith queue is an exponentially distributed random variable with rate μi. Whenever two or more customers are in the system, the decision as to which customer should be served first depends on the optimzation criterion. In this system all server allocation policies in the finite set of work conserving deterministic policies have the same expected first passage times (makespan) to empty the system of customers from any initial state. However, a unique policy maximizes the first passage probability of empty-ing the system before the number of customers exceeds K, for any value of K, and it stochastically minimizes (he number of customers in the system at any time t > 0 . This policy always assigns the server to the non empty queue closest to the exit

Abstract: The memory comprises a linear space and a buffered space, each page of the buffered space is divided in a number m+1 of buffers of equal capacity, with m buffers devoted to the storage of data and one control buffer divided into m control blocks. There is a fixed relationship between one buffer control block and one data buffer. The control blocks are devoted to the storage of buffer and message chaining information. The linear space comprises queue control blocks, with one queue control block per user. The messages are received by memory interface 22 from the source users and then are enqueued in link inbound queues (LIQ) which are dynamically built by taking buffers from the buffered space, chaining the buffers by writing buffer and message chaining information in the corresponding buffer control blocks and writing the queue head and queue tail addresses in the user queue control block. A centralized control means is designed to process enqueue, dequeue and release orders upon requests from a user selected by an arbitrating means. When a link inbound queue becomes not empty, the memory interface 22 sends a dequeue order request to the centralized control means, said request identifying the corresponding user queue control block. The message address is provided in response thereto with the identification of the queue control block of the destination user. Then, the memory interface 22 sends an enqueue request to the centralized control means, said request identifying the address of the message to be enqueued and the queue control block of the destination user. The processing of this enqueue request by the centralized control means causes the messages to be enqueued in an outbound queue from which it is transferred to the destination user, by memory interface 22.

Abstract: An approximate performance evaluation technique for analyzing load-dependent interactive queueing systems is proposed. The service stations in the queuing system are heterogeneous., i.e. they have different service rates. As an example, the authors apply this analytical method to a recently proposed receiver-initiated dynamic load balancing scheme in a multiple-station distributed heterogeneous computer system. This performance model attempts to obtain approximations to the steady-state distribution of the average system response time for a multiple-node heterogeneous scenario. The results are validated using a GPSS (general-purpose system simulation) model. Comparison between this approximation model and the simulation results show excellent agreement. The performance of the ERIDA scheme is compared with the no-load-sharing case and also with a centralized load-balancing scheme. These latter systems provide lower and upper bounds on performance of a distributed and sharing scheme. >

Abstract: The performance analysis of ring type LANS has received much attention. The advantage of the ring type architecture is due to the fact that it is particularly suitable for the transport of real time traffic with guaranteed time delay performance. However, it can be shown that uncontrolled rings are unstable in the sense that the Markov chain that describes the behavior has adsorbing states which amount to deadlock. Thus, a natural question that arises is the control of ring type architectures. Motivated by this question, the authors consider a system of two coupled queues where a packet after being served in one queue can be fed into the other queue or leave the system. In addition there are external Poisson arrivals at each queue. These can in general be optimally controlled by applying a probabilistic rule minimizing an average discounted cost which is a linear function of the total amount of blocking as well as the number of packets in the system. It is shown that the optimal blocking mechanism is deterministic (bang-bang) and is characterized by two monotone switching curves in the state space associated with the system. The approach used relies on Markov decision theory and convexity arguments. >

Abstract: An analysis is provided of queuing models in virtual route networks for which a pacing window flow control mechanism is used. An input queue is introduced to describe the waiting system where messages prevented from entering the network are stored in first-come, first-served manner. Both finite and infinite capacity are considered. The model leads to a Markovian queuing system, which is fully solved by matrix-geometric methods. The analytical results show that the optimal window size which maximizes the power criterion including the admission delay is nearly twice the number of hops (nodes of the network) for the model with infinite input-queue capacity. This rule of thumb also applies to the finite-capacity model with certain restrictions. Simulations are presented to verify the analytical results. >

Abstract: Subcarrier audio channels (SCAs) are used to support a wide-area data communication system. Text or data messages can be transmitted nationally using satellite delivery, and locally using FM broadcasting stations' subcarriers. The time delay that messages experience in the national buffer at the satellite head-end or the local buffer is examined. The delay for various throughput data rates is evaluated to identify an optimum range for this capacity. A realistic set of messages statistics is developed to model SCA traffic. Three different queueing strategies are used to examine the delay that messages obeying these statistics would experience: first-come-first-served, fixed-priority, and delay-dependent priority. It is shown that, as the throughput is increased, the effect of priority on the system is less discernible. As the output capacity is decreased, the effect of a priority structure can be seen to enhance traffic flow. Total message time delay is examined using a delay-dependent priority scheme. Results indicate that the choice of an appropriate queuing strategy will enhance the flow of priority message traffic. >

Abstract: A single clock-regulated queue is fed by two Bernouilli streams of messages. We present the distributions of queue length, of waiting time, and of output for such a system. This is generalized as well to the case of a queue of finite capacity.

Abstract: Given an M/G/1 queue, a special customer, and an exponential random variable M that is independent of the queueing process, if the special customer reaches the front of the queue before the time specified by M, it cannot be processed and must re-enter the queue at the back. While waiting in the queue, the available decisions for the special customer are either to keep its position in the queue or to leave its position to join the back of the queue. The author's goal is to find a strategy that minimizes the expected delay until the special customer starts being processed. The move-along policy is to always stay in the queue until the front of the queue is reached, and if it cannot be served, to join the back of the queue. The basic result is that if the queue is stable, the move-along policy is optimal. >

Abstract: PURPOSE:To give a higher real time characteristic even to the task of a low priority level while the real time characteristic of the task of a high priority level is secured by making the priority level of the low task of the priority level higher at every time it exceeds an arbitrary time CONSTITUTION:When a controller 8 receives an interruption signal, the contents of a time register table 4 and the present time of a timer 1 are compared by a comparator 5 At the time of the coincidence after the result of the comparison, a task control block TCB in a queue management table 7 is made higher by one level, and this is registered newly to the trailing end of the queue Thus, to the task in which activating is awaited for a long time, a high priority level is given Consequently, even the task of the low priority level can secure the higher real time property

Abstract: An algorithmic method is introduced to calculate the waiting-time probability density function in a static priority queue with more than two priorities. The solution for a two-level queuing system is used as the stepping stone for the derivations. Also, a priority-based computer network is introduced to which the obtained results are directly applicable. >

Abstract: A new priority queue implementation for the future event set problem is described in this article. The new implementation is shown experimentally to be O(Z) in queue size for the priority increment distributions recently considered by Jones in his review article. It displays hold times three times shorter than splay trees for a queue size of 10,000 events. The new implementation, called a calendar queue, is a very simple structure of the multiple list variety using a novel solution to the overflow problem.

Abstract: We study the queueing system Geometric/G/1/N with state-dependent arrival rates in discrete time. We develop a stable algorithm for computing the stationary waiting time distribution with respect to an entering customer.

Abstract: The analysis of simulation data often calls for a test of the equality of means (medians) of several sets of data, which may not meet the classical assumptions of the analysis of variance (ANOVA) test procedures. This paper compares two parametric ANOVA tests and two nonparametric tests, with and without blocking on common random numbers. The test data was obtained from average queue waiting times in an M/M/c queuing system. The parametric ANOVA tests had significantly larger test statistic values than the nonparametric tests. The parametric tests showed the ability to detect different queue waiting times at least as well as their non-parametric counterparts, even though the assumptions of the parametric ANOVA tests are not met with the non-normally distributed queueing system data

Abstract: A bulk arrival M/sup x//M/c queuing system is used to model a centralized parallel processing system with job splitting. In such a system, jobs wait in a central queue, which is accessible by all the processors, and are split into independent tasks that can be executed on separate processors. The job response-time consists of three components: queuing delay, service time, and synchronization delay. An expression for the mean job response-time is obtained for this centralized parallel-processing system. Centralized and distributed parallel-processing systems (with and without job-splitting) are considered and their performances compared. Furthermore, the effects of parallelism and overheads due to job-splitting are investigated. >

Abstract: A new priority queue implementation for the future event set problem is described in this article. The new implementation is shown experimentally to be O(1) in queue size for the priority increment distributions recently considered by Jones in his review article. It displays hold times three times shorter than splay trees for a queue size of 10,000 events. The new implementation, called a calendar queue, is a very simple structure of the multiple list variety using a novel solution to the overflow problem.