Jingui Xie

On the stationary distribution of queue lengths in a multi-class priority queueing system with customer transfers

This paper deals with a multi-class priority queueing system with customer transfers that occur only from lower priority queues to higher priority queues. Conditions for the queueing system to be stable/unstable are obtained. An auxiliary queueing system is introduced, for which an explicit product-form solution is found for the stationary distribution of queue lengths. Sample path relationships between the queue lengths in the original queueing system and the auxiliary queueing system are obtained, which lead to bounds on the stationary distribution of the queue lengths in the original queueing system. Using matrix-analytic methods, it is shown that the tail asymptotics of the stationary distribution is exact geometric, if the queue with the highest priority is overloaded.

Stability of a priority queueing system with customer transfers

This paper is concerned with the stability of a preemptive priority queueing system with customer transfers. Conditions for the queueing system to be stable/unstable are found. An interesting result is that the stability/instability conditions are independent of the service rates of lower priority customers and the transfer rates.

Algorithmic prediction of individual diseases

The enormous and increasing cost of health care is burdensome for most low- to middle-income families, especially those families whose members are battling chronic diseases. If effective interventions can be conducted at earlier stages, many costs are avoidable. Correspondingly, predicting the future disease one patient may develop with accuracy is a crucial step towards solving this problem. We have developed a system called CAC, which integrates Clustering, Association analysis and Collaborative filtering to predict patients’ future conditions. The data-set used in this study is health insurance data collected from a provincial capital city of China. Specifically, the data-set includes 151,237 insured patients who have reimbursement records between 2007 and 2014. The patients are artificially classified into acute patients and chronic patients. For both sets of patients, we utilise a training set to generate the prediction rules and a testing set to test the prediction results. The results show that for 71% of acute patients and 82% of chronic patients, their future conditions are predictable.

Determining the conditions for reverse triage in emergency medical services using queuing theory

In emergency health care, there are situations where the less wounded are treated in preference to the more severely wounded, so called reverse triage. This may arise in situations such as war where soldiers are required to return to the battlefield as quickly as possible, or disaster situations where medical resources are limited in order to conserve resources for those likely to survive without requiring advanced medical care. This article is to study the reverse triage in time-critical systems, where conditions of patients may deteriorate while waiting for treatment. A queueing model with transfers and abandonments is developed to study the health care system. Using smoothed rate truncation method, sufficient conditions of reverse triage are derived, under which non-critical patients are treated with priority. For other conditions, the optimal policy is very complicated. We suggest a dynamic control policy according to the system state rather than any static priority policies.

Performance analysis of service systems with priority upgrades

In this paper, we study the performance of service systems with priority upgrades. We model the service system as a single-server two-class priority queue, with queue 1 as the normal queue and queue 2 as the priority queue. The queueing model of interest has various applications in healthcare services, perishable inventory and project management. We comprehensively examine the system’s stationary distribution, computational algorithm design and sensitivity analysis. We observe that when queue 2 is large, the conditional distribution of queue 1 approximates a Poisson distribution. The tail probability of queue 2 decays geometrically, while the tail probability of queue 1 decays much faster than queue 2’s. This helps us design an algorithm that computed the stationary distribution. Finally, by using the algorithm, we perform a sensitivity analysis on various system parameters, i.e., the arrival rates, service rates and the upgrade rate. The numerical study provides helpful insights into designing such service systems.

Dynamic control of a tandem system with abandonments

The goal of this paper is to provide a model that is an extension of classic scheduling problems for a tandem queueing system by including customer impatience. In such scenarios, the server(s) must balance abandonments from each phase of service with the need to prioritize higher reward customers. This presents an interesting challenge since the trade-off between the cost of abandonments and revenue maximization is not at all clear. As a result of customer abandonments, traditional solution techniques are not available. In particular, uniformization is not possible since the transition rates are unbounded. We do our analysis in continuous time, using the continuous-time Markov decision process framework to discern simple relationships of the value functions depending on the starting state. We then use sample path arguments to analyze the structure of the optimal policy. We provide conditions under which an optimal policy is nonidling and never splits servers (except to avoid idling). We then consider the single-server model as a proxy for the decision problem when there are more customers at each station than there are servers. In this case, we provide conditions under which it is optimal to prioritize each station.

Optimal Control of an Inventory System With Joint Production and Pricing Decisions

In this study, we consider a stochastic inventory system in which the objective of the manufacturer is to maximize the long-run average profit by dynamically offering the selling price and switching the production on or off. The demand process is non-homogeneous Poisson with a price-dependent arrival rate. System costs consist of switching costs, inventory holding and backlogging costs. We show that an (s,S,p) policy is optimal. Moreover, we characterize the structural properties of the optimal profit function and pricing strategy, and show that the optimal price is a quasiconcave function of the inventory level when the production is off and is a quasiconvex function when the production is on.

Cyclic Change of Server's Performance: Impacts and Applications

This paper studies a stochastic system where the performance of the server changes stochastically and cyclically. We first investigate the performance measures of the system, including the queue length and the overall cost. In particular, we derive an exact expression for the expected length of the renewal cycle, and present closed matrix forms for the mean and variance of the queue length. We then develop an explicit method to tackle a workload control problem, based on an M/G/1 queue approximation. Numerical examples are presented to illustrate the effectiveness of the method.