Mean Number Of Customers Research Articles

G/ Gy/ m queueing system with discouragement via diffusion approximation

This paper provides an approximation technique for a G/ G y / m queueing system with discouragement. The approximation is based on the theory of diffusion, depending on the means and variances of interarrival time and service time distributions. The arriving customers are assumed to be discouraged when a large number of customers are present in the system. The expressions for the probability of there being n customers in the system and the mean number of customers in the system, are obtained.

Optimal dispatch of a two-terminal shuttle system

We consider two batch service queues served by a common carrier with capacity C operating between them. Passengers arrive at these terminals according to independent Poisson processes. Travel times are independent and exponentially distributed with mean parameters μ1 μ2 shuttling customers between the two queues. With complete decomposition of the system and a general bulk service rule at one queue, we provide an expression for the mean number of customers waiting at each queue. We also examine a search procedure to obtain the threshold level which minimizes the mean number of waiting customers

Invariance of the mean number of customers in priority queueing systems with a finite source

Invariance of the mean number of customers in priority queueing systems with a finite source

Information theoretic analysis for a general queueing system at equilibrium with application to queues in tandem

In this paper, information theoretic inference methology for system modeling is applied to estimate the probability distribution for the number of customers in a general, single server queueing system with infinite capacity utilized by an infinite customer population. Limited to knowledge of only the mean number of customers and system equilibrium, entropy maximization is used to obtain an approximation for the number of customers in the G¦ G¦1 queue. This maximum entropy approximation is exact for the case of G=M, i.e., the M¦M¦1 queue. Subject to both independent and dependent information, an estimate for the joint customer distribution for queueing systems in tandem is presented. Based on the simulation of two queues in tandem, numerical comparisons of the joint maximum entropy distribution is given. These results serve to establish the validity of the inference technique and as an introduction to information theoretic approximation to queueing networks.

Maximum Entropy Condition in Queueing Theory

The main results in queueing theory are obtained when the queueing system is in a steady-state condition and if the requirements of a birth-and-death stochastic process are satisfied. The aim of this paper is to obtain a probabilistic model when the queueing system is in a maximum entropy condition. For applying the entropic approach, the only information required is represented by mean values (mean arrival rates, mean service rates, the mean number of customers in the system). For some one-server queueing systems, when the expected number of customers is given, the maximum entropy condition gives the same probability distribution of the possible states of the system as the birth-and-death process applied to an M/M/1 system in a steady-state condition. For other queueing systems, as M/G/1 for instance, the entropic approach gives a simple probability distribution of possible states, while no close expression for such a probability distribution is known in the general framework of a birth-and-death process.

Some Equivalence Results for Load-Independent Exponential Queueing Networks

In this paper we derive a number of results concerning the behavior of closed load-independent exponential queueing networks. It is shown that if the service rate of any station is increased (decreased), then the throughput of the network itself also increases (decreases). This is not true for product form networks in general. In addition, if the service rate at server i is increased then both the mean queue length and mean waiting time at server i decrease while both these quantities increase at all stations j ? i. The opposite effect is observed if the senrvice rate at station i is decreased. The main result of the paper is a proof of the conjective that corresponding to any general closed queueing network consisting of M stations and in which N customers circulate according to the elements of an irreducible stochastic routing matrix Q, there exists a closed load-independent exponential queueing network with the same M, N, and Q such that the mean number of customers at each station in the exponential network is equal to that in the general network. If the network throughput is specified, it is shown that this exponential network iS unique.

有限の待ち合い室を有するGI/E_k/1待ち行列システム

The GI/Ek/l queue with fmite waiting room is investigated by using a combination of the supplementary variable and phase techniques. We start by studying the steady·state joint distribution .of the number of phases present and the elapsed time since the last arrival. From this distribution, we obtain the distributions of the number of customers both at an arbitrary moment and just after an arrival. Furthermore, we show some interesting properties on the mean number of customers from numerical examples.

ボーキングのある複数窓口待ち行列問題の拡散近似法

This paper deals with the diffusion approximation technique for solving multi-server queueing problems with balking having Erlangian inter-arrival time and Erlangian service time distributions. Probability of joining of a new customer to the system is assumed to vary as e^<-γy> where γ is a positive parameter and y is the queue length. The approximation technique is based on the theory of diffusion, considering only means and variances of arrival and departure processes. Approximate formulas for P (n), probability of finding n customers in the system, and L, mean number of customers in the system, at steady state, are given. Finally, comparisons of approximate and exact or simulated values of mean number L of customers in the system are made for some E_l/E_k/s (∞) systems with balking to show the effectiveness of the approximation technique and graphs of approximate values of L for several systems are drawn which can be used in practice.

Finite Queues in Series with Exponential or Erlang Service Times—A Numerical Approach

This paper considers a queuing system consisting of N service channels in series where each channel has an exponential or Erlang holding time and (except for the first channel) a finite queue, and where the input process is such that the first queue is never empty. The measures considered are the steady-state mean output rate and mean number of customers in the system (excluding the first queue). First, a procedure is described, for obtaining these measures, that is relatively efficient computationally. Second, an exceptionally efficient procedure is developed for approximating the mean output rate for the case of exponential holding times. It is demonstrated that this procedure provides an excellent approximation for most cases and that it is computationally feasible for large problems. Third, extensive new numerical results are obtained.