An M/G/1 Retrial Queueing System with Two-Phase Service and Preemptive Resume

An M/G/1 retrial queueing system with additional phase of service and possible preemptive resume service discipline is considered. For an arbitrarily distributed retrial time distribution, the necessary and sufficient condition for the system stability is obtained, assuming that only the customer at the head of the orbit has priority access to the server. The steady-state distributions of the server state and the number of customers in the orbit are obtained along with other performance measures. The effects of various parameters on the system performance are analysed numerically. A general decomposition law for this retrial queueing system is established.     

Index Heuristics for Multiclass M/G/1 Systems with Nonpreemptive Service and Convex Holding Costs

We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.     

Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks

We consider multiclass feedforward queueing networks under first in first out and priority service disciplines driven by long-range dependent arrival and service time processes. We show that in critical loading the normalized workload, queue length and sojourn time processes can converge to a multi-dimensional reflected fractional Brownian motion. This weak heavy traffic approximation is deduced from a deterministic pathwise approximation of the network behavior close to constant critical load in terms of the solution of a Skorokhod problem. Since we model the doubly infinite time interval, our results directly cover the stationary case.AMS subject classification: primary 90B15, secondary 60K25, 68M20     

Polling systems in heavy traffic: Exhaustiveness of service policies

We study the expected delay in cyclic polling models with general ‘branching-type’ service disciplines. For this class of models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the expected delay under standard heavy-traffic scalings. We identify a single parameter associated with the service discipline at each queue, which we call the ‘exhaustiveness’. We show that the scaled expected delay figures depend on the service policies at the queues only through the exhaustiveness of each of the service disciplines. This implies that the influence of different service disciplines, but with the same exhaustiveness, on the expected delays at the queues becomes the same when the system reaches saturation. This observation leads to a new classification of the service disciplines. In addition, we show monotonicity of the scaled expected delays with respect to the exhaustiveness of the service disciplines. This induces a complete ordering in terms of efficiency of the service disciplines. The results also lead to new rules for optimization of the system performance with respect to the service disciplines at the queues. Further, the exact asymptotic results suggest simple expected waiting-time approximations for polling models in heavy traffic. Numerical experiments show that the accuracy of the approximations is excellent for practical heavy-traffic scenarios. This revised version was published online in June 2006 with corrections to the Cover Date.     

示波极谱法测定保健药品中的褪黑激素

褪黑激素与HNO3在室温下发生硝基化反应生成褪黑激素的硝基化合物,加NH3·H2O终止反应并用甲酸 甲酸钠缓冲液控制反应液pH3,在原点电位-0.20V(vs.SCE),测量-0.50V处的二阶导数峰高。方法检出限为1μg/L,线性范围为1μg/L～200μg/L,相对标准偏差为2.6%～8.0%,加标回收率为92 0%～110 0%,测定结果与高效液相色谱法进行比较,无显著性差异。     

M/G/1/N vacation model with varying E-limited service discipline

We define and analyze anM/G/1/N vacation model that uses a service discipline that we call theE-limited with limit variation discipline. According to this discipline, the server provides service until either the system is emptied (i.e. exhausted) or a randomly chosen limit ofl customers has been served. The server then goes on a vacation before returning to service the queue again. The queue length distribution and the Laplace-Stieltjes transforms of the waiting time, busy period and cycle time distributions are found. Further, an expression for the mean waiting time is developed. Several previously analyzed service disciplines, including Bernoulli scheduling, nonexhaustive service and limited service, are special cases of the general varying limit discipline that is analyzed in this paper.     

A duality relation for busy cycles inGI/G/1 queues

Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint distribution of several variables associated with the busy cycle inM/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dualGI/M/1. In this note, we generalize this duality relation toGI/G/1 queues with modified first services; this clarifies the original result, and shows that the generalized ballot theorem is superfluous for the duality relation.     

Stationary remaining service time conditional on queue length

In Mandelbaum and Yechiali [The conditional residual service time in the M/G/1 queue, http://www.math.tau.ac.il/∼uriy/publications (No. 30a), 1979] and in Fakinos [The expected remaining service time in a single-server queue, Oper. Res. 30 (1982) 1014-1018] a simple formula is derived for the (stationary) expected remaining service time in a M/G/1 queue, conditional on the number of customers in the system. We give a short new proof of the formula using Rate Conservation Law, and generalize to handle higher moments.     

Practical aspects associated with location planning for maternal and perinatal assistance in Brazil

A study has been carried out aimed at reducing perinatal mortality in the municipality of Rio de Janeiro through a better distribution of health care facilities. The algorithmic aspects are detailed elsewhere and here the emphasis is on practical issues and difficulties encountered. A 3-level hierarchical model was developed. Both uncapacitated and capacitated versions are briefly described together with some results based on actual data. The project brought to light many contradictions between OR theory and practice in developing countries and, unfortunately, the models developed were not implemented by the municipality health authorities. Possible reasons for this outcome are analysed.     

On the validity and utility of queueing models of human service systems

Based on observations made during an extensive study of police patrol operations in New York City, we examine the issues of the validity and utility of queueing models of service systems in which adaptive behavior by the (human) customers or servers is likely. We find that in addition to depending on the technical accuracy of its assumptions, the accuracy of such a model will also depend upon the level of managerial control of the system and adequacy of resources. We recommend that queueing models of human service systems be used in a normative fashion and incorporated in the management feedback loop.