Remarks on the remaining service time upon reaching a target level in the M/G/1 queue

In this note we establish connections between new and previous results on the remaining service time upon reaching a target level in the M/G/1 queue.     

Analysis of a discrete-time queueing system with time-limited service

We analyze a discrete-time, single-server queueing system in which the length of each service period is limited. The server takes a vacation when the limit expires or the queue empties, whichever occurs first. In the former case, the preempted service is resumed after the vacation without loss or creation of any work. This system models the transmission of message frames from a station on timed-token local-area networks (for example, FDDI and IEEE 802.4 token bus). We study the process of the unfinished work and the joint process of the queue size and the remaining service time. By using the technique of discrete Fourier transforms to determine some unknown functions in the governing equations, we numerically obtain exact mean waiting times.A part of the work of H. Takagi was done while he was with IBM Research, Tokyo Research Laboratory.     

A complete and simple solution for a discrete-time multi-server queue with bulk arrivals and deterministic service times

A complete distribution for the system content of a discrete-time multi-server queue with an infinite buffer is presented, where each customer arriving in a group requires a deterministic service time that could be greater than one slot. In addition, when the service time equals one slot, a complete distribution for the delay is also presented.     

服务员假期中以概率p进入的M/G/1排队系统的随机分解

该文研究M/G/1多重休假排队系统，其中在服务员休假中到达顾客以概率p(0≤p≤1)进入。通过引进“服务员忙期”和使用拉普拉斯变换或拉普拉斯— —司梯阶变换，我们获得队长瞬态分布的拉普拉斯变换和稳态分布的递推表达式，进一步得到稳态队长分布的随机分解和在特殊情况下相应的一些结果。     

Performance analysis of GI/M/1 queue with working vacations and vacation interruption

In this paper, we analyze a single-server vacation queue with a general arrival process. Two policies, working vacation and vacation interruption, are connected to model some practical problems. The GI/M/1 queue with such two policies is described and by the matrix analysis method, we obtain various performance measures such as mean queue length and waiting time. Finally, using some numerical examples, we present the parameter effect on the performance measures and establish the cost and profit functions to analyze the optimal service rate η during the vacation period.     

Performance analysis of MAP/G/1 queue with working vacations and vacation interruption

We consider the MAP/G/1 queue with working vacations and vacation interruption. We obtain the queue length distribution with the method of supplementary variable, combined with the matrix-analytic method and censoring technique. We also obtain the system size distribution at pre-arrival epoch and the Laplace–Stieltjes transform (LST) of waiting time.     

A bulk arrival queueing model with fuzzy parameters and varying batch sizes

This paper develops a nonlinear programming approach to derive the membership functions of the steady-state performance measures in bulk arrival queueing systems with varying batch sizes, in that the arrival rate and service rate are fuzzy numbers. The basic idea is based on Zadeh’s extension principle. Two pairs of mixed integer nonlinear programs (MINLP) with binary variables are formulated to calculate the upper and lower bounds of the system performance measure at possibility level α. From different values of α, the membership function of the system performance measure is constructed. For practice use, the defuzzification of performance measures is also provided via Yager ranking index. To demonstrate the validity of the proposed method, a numerical example is solved successfully.     

M/M/1 Queueing systems with inventory

We derive stationary distributions of joint queue length and inventory processes in explicit product form for various M/M/1-systems with inventory under continuous review and different inventory management policies, and with lost sales. Demand is Poisson, service times and lead times are exponentially distributed. These distributions are used to calculate performance measures of the respective systems. In case of infinite waiting room the key result is that the limiting distributions of the queue length processes are the same as in the classical M/M/1/∞-system. All authors were supported by DAAD/KBN grant number D/02/32206.     

Queue lengths and workloads in polling systems

For a single-server multi-station polling system, we focus on the generating function and Laplace–Stieltjes transform of the time-stationary joint queue length and workload distributions, respectively, under no further assumptions on the service discipline. We express these quantities as expressions involving the generating functions of the joint queue length distribution at visit beginnings and visit completions at the various stations. The latter is known for a broad variety of cases. Finally, we identify a workload decomposition result.     

Performance Analysis of a Finite-Buffer Bulk-Arrival and Bulk-Service Queue with Variable Server Capacity

Abstract

In this paper, we consider a finite-buffer bulk-arrival and bulk-service queue with variable server capacity: M ^X /G ^Y /1/K + B. The main purpose of this paper is to discuss the analytic and computational aspects of this system. We first derive steady-state departure-epoch probabilities based on the embedded Markov chain method. Next, we demonstrate two numerically stable relationships for the steady-state probabilities of the queue lengths at three different epochs: departure, random, and arrival. Finally, based on these relationships, we present various useful performance measures of interest such as moments of the number of customers in the queue at three different epochs, the loss probability, and the probability that server is busy. Numerical results are presented for a deterministic service-time distribution – a case that has gained importance in recent years.