A batchSPP/G/1 queue with multiple vacations and exhaustive service discipline

This paper considers a batch-arrival single-server queueing system with multiple vacations and exhaustive service discipline. Customers arrive to the system in accordance with a batch switched Poisson process (batchSPP). Using the supplementary variable technique, we analyze the stationary queue length distribution and derive various formulas for queue lengths and waiting times. In particular, we analytically show the decomposition property for the waiting time distributions. Therefore, the waiting time formulas developed in this paper can also be applied to a batchSPP/G/1 queue without vacations.     

Burst ratio in a single-server queue

Telecommunication Systems - In contemporary packet networks, the possibility of packet loss is a negative, but inevitable aspect of the network design. One of the most important characteristics of...     

Cyclic-service systems with nonpreemptive, time-limited service

We analyze an asymmetric cyclic-service system with multiple queues and nonpreemptive, time-limited service. The time limit for a server visit at each queue is exponentially distributed. Customer service times and changeover times have general distributions. Using discrete Fourier transforms, the queue-length and delay distributions are solved     

Analysis of a discrete-time single-server queue with bursty inputsfor traffic control in ATM networks

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     

The single-server Markovian overflow queue with balking, reneging and an additional server for longer queues

The aim of this paper is to treat an analytical explicit solution of the moments of a system of an overflow queue (M/M/1/k, M/M/∞), with the balking, reneging and an additional server for longer queues. An explicit solution for M₍₁₎, M₍₂₎ and M_(l) is given. Finally, we deduce some particular cases for the two systems (M/M/1/k, M/M/∞) and (M/M/2/k, M/M/∞).     

带有服务中断的周期到达队列的模拟仿真

文中运用连续时间离散化的思想,设计了一种带有服务中断的多服务器系统的仿真算法。将周期到达队列模型与服务中断结合起来,在高负荷的条件下,通过Matlab编程,模拟带有服务中断的Mt/M/n模型,为多服务台排队模型的模拟仿真提供了一种新思路。通过修改随机数产生方法和限制条件模型可以拓展到G/M/n+M,G/M/n/K+M模型等。     

A renewable single-server queueing system with priorities

A single-server queue with a triple priority system is considered in this paper. The server can fail during its occupation time and is sent for repair immediately.The stationary probabilities of the different states of the system are studied, under the assumption that the arrival time and the service time for the three kinds of customers, and the repair time, all have Poisson distributions with different parameters. The results obtained before, in [Mokaddis et al., Eighth International Congress for Statistics, Computer Science, Social and Demographic Research, Vol. 4, pp. 31–58 (1983)] in the case of a double priority, are derived from the present results as special cases. Moreover the mathematical expectation of the number of customers and the average waiting time of both kinds of customers and more characteristics of the system, in the case of double priority, are obtained. Also, in this paper, we study the system without priority, in the cases of both a triple priority system and a double priority system.     

Analysis of demand‐priority access using a priority queue with server vacations and message dependent switchover times

In this paper, we analyse the message waiting times in a local area network (LAN) that uses the demand‐priority access method. This is a priority‐based round‐robin arbitration method where the central controller (the repeater) polls its connected ports to determine which have transmission requests pending and the requests' priority classes. We model it as a 2‐priority M/G/1 queue with multiple server vacations and switchover time between service periods. The service discipline is nonpreemptive and the length of the switchover time is dependent upon the priority class of the preceding message served as well as that of the message to be served next. We provide an approximate analysis for the waiting times of both message classes and derive expressions for the Laplace–Stieltjes transforms (LST) of the stationary distributions and the mean waiting times. We conclude with numerical and simulation results to show the applicability and accuracy of the analytical model. This revised version was published online in June 2006 with corrections to the Cover Date.     

Tandem queue with three multiserver units and bulk service in unit III

In this paper a queueing model consisting of three units in series, with a finite number of parallel servers at each unit, is considered. Buffers of nonidentical finite capacity are available between the units. A buffer of infinite capacity is assumed to exist in front of the first unit. The occurrence times for all events have negative exponential distributions. Customers in the units I and II are served singly. Customers in the buffer zone between units II and III are served according to the general bulk service rule. The service times in the ith unit (i = 1, 2, 3) are assumed to be independently identically distributed random variables with negative exponential distributions with parameters μ_i(i = 1, 2, 3). The steady state probability vector of the number of customers in the queue is obtained using a modified matrix-geometric method. The stability condition is also obtained.     

基于开源的消息队列云服务研究

随着互联网应用软件规模的不断增长,分布式架构成为了应用开发的主流模式,而消息队列解决了分布式应用之间的通信难题,开源的推动使得消息队列成为了快速发展的热点技术.同时,云计算经过十余年的发展,逐渐从提供IT基础设施向应用开发渗透,国内主流的云服务商基于开源的消息队列技术推出了各自的消息队列云服务,如何评估这些云产品的功能和性能,给用户提供客观准确的参考,从而推动云计算市场积极发展,是当前亟待解决的重要问题.首先介绍了当前主流的开源消息队列产品及其特点,然后分析研究了云服务化的消息队列产品的特征,最后分析了消息队列云服务的性能测试指标,为企业及个人用户选型提供了参考意见.     

Analysis of an M/G/1/N queue with vacations and its iterativeapplication to FDDI timed-token rings

We present the analysis of an M/G/1/N queueing system with vacations under a dynamic time-limited service policy. This method is used to develop a procedure for performance analysis of a fiber distributed data interface (FDDI) network serving buffer-limited stations under asynchronous service. An efficient iteration procedure is employed to evaluate the limiting state distribution of the embedded Markov chain representing the system state process. Using supplementary variables and sample biasing techniques, we derive the queue size distribution at an arbitrary instant of time as well as the packet blocking probability and the mean packet delay. By exploiting the subtle structure of conditional supplementary variables and the recursive property of the conditional residual delay, the Laplace-Stieltjes transform of the packet delay distribution and a time-domain approximation of the packet delay distribution are obtained. For the analysis of a heterogeneous multi-station FDDI network, an iterative procedure which uses repeatedly the M/G/1/N vacation model described above is presented. This procedure provides for a numerically efficient analysis method by employing constructions of the approximate vacation time distributions. We illustrate the application of our analytical techniques to both symmetric and nonsymmetric FDDI network systems     

An additional space special service facility heterogeneous queue

In this paper we consider steady-state behaviour of a heterogeneous queueing system with instantaneously available special service facility and probabilistically available additional space both of which are queue-length dependent. The system operates at two different levels. The arrivals and the departures at these two levels occur at different rates. Steady-state probabilities at both the levels are calculated explicitly. Average number of customers in the system is also obtained. Associating the various costs, a criterion to obtain the decision points at which the hiring of additional space will be profitable and that for the size of additional space to be hired is discussed.     

A VLSI priority packet queue with inheritance and overwrite

Reliable priority-based flow-control is essential for real-time applications involving hard-deadlines. However, the use of first-in-first-out (FIFO) queues in such systems introduces priority inversion resulting in unbounded transmission delays. For this reason, a priority transmission queue is critical for multimedia and mission-critical systems. Yet very few priority queue implementations exist. This paper presents the design of a novel VLSI priority packet queue (PPQ), implemented in 1.2 μm CMOS technology. It achieves fast operation by manipulating its contents in terms of packet segments, rather than individual words. Similar to paged memory, this new segmented architecture greatly reduces implementation cost by reusing segments and avoiding storage area fragmentation. By distributing the computationally intensive priority comparison operation over the access time for an entire segment, the PPQ achieves 96% of the speed of a high-speed packet FIFO. The PPQ can either perform priority inheritance or overwrite lower priority packets to minimize the impact of queue overflow. In addition, it is suitable as a general computer network interface buffer, since it robustly handles asynchronous read and write clocks of greatly disparate frequencies. Our initial implementation achieves well over twice the speed of a nonpipelined approach with minimal additional overhead. Furthermore, scaling this design to larger capacities and more priority levels results in an even greater improvement in speed over conventional approaches     

Approximating the heterogeneous fluid queue with a birth-deathfluid queue

Recent research has shown that fluid-flow queueing models accurately determine the burst level component of the ATM multiplexer process, and fluid models therefore constitute an efficient tool for the investigation of admission control in ATM networks. This article first gives a review of Markov-driven fluid queues with special attention given to the heterogeneous on/off model. Then an approximation procedure in which the original heterogeneous arrival process is replaced by a homogeneous birth-death arrival process is presented. The substitution is based on matching statistical parameters. Finally, the approach is evaluated by numerical examples     

Construction of time-limited functions with specified autocorrelation functions

A necessary and sufficient condition is derived for a function to be the autocorrelation function of a time-limited function of specified length. A constructive procedure for determining all possible time-limited functions having the same autocorrelation function as a given time4imited function is presented. The procedure consists of passing the given time function through one out of a collection of specially tailored all-pass filters. The class of functions so generated may be either finite or infinite depending on the original time function. Specific examples of the construction procedure are given.     

Explicit transient and steady state queue length probabilities of a queueing model with server on vacation providing service intermittently

The present paper studies the transient and steady state behaviour of a first-come-first-served, single channel queueing problem with server on vacation providing service intermittently. Laplace transforms of explicit queue length probabilities are obtained by solving the difference equations recursively. Particular cases of interest are also derived.     

Adaptive mean queue size and its rate of change: queue management with random dropping

The random early detection active queue management (AQM) scheme uses the average queue size to calculate the dropping probability in terms of minimum and maximum thresholds. The effect of heavy load enhances the frequency of crossing the maximum threshold value resulting in frequent dropping of the packets. An adaptive queue management with random dropping algorithm is proposed which incorporates information not just about the average queue size but also the rate of change of the same. Introducing an adaptively changing threshold level that falls in between lower and upper thresholds, our algorithm demonstrates that these additional features significantly improve the system performance in terms of throughput, average queue size, utilization and queuing delay in relation to the existing AQM algorithms.     

A discrete time-limited vacation model for the fair share scheduler

We present a vacation model which can be used as a component of the type of polling system encountered in a fair share scheduler. Consider two queues in tandem attended by one server. The primary queue Q _p, which has an infinite buffer, has a preemptive priority over the secondary queue Q _s which has a finite buffer. Jobs which complete service at the primary queue will go into the secondary queue for another service with a probability p. The server visits Q _s for a maximum of T units of time. After visiting for T units of time or after Q _s becomes empty, whichever occurs first, the server goes on a vacation. The duration of this vacation has a phase type distribution. The vacation can also be interrupted in order to attend to the jobs in Q _p. The resulting Markov chain describing this system is of the QBD type. We show that the resulting R matrix associated with this Markov chain has a very special structure which reduces to the solution of a smaller dimension matrix. We then show how to obtain the key performance measures for this system. Of interest is the approach used for obtaining the waiting time distribution. Some numerical examples are also presented. This revised version was published online in June 2006 with corrections to the Cover Date.