Motivated by the patient triage problem in emergency response, we consider a single-server clearing system in which jobs might abandon the system if they are not taken into service within their “lifetime.” In this system, jobs are characterized by their lifetime and service time distributions. Our objective is to dynamically determine the optimal or near-optimal order of service for jobs so as to minimize the total number of abandonments. We first show that if the jobs can be ordered in such a way that the job with the shortest lifetime (in the sense of hazard rate ordering) also has the shortest service time (in the sense of likelihood ratio ordering), then the optimal policy gives the highest priority to this “time-critical” job independently of the system state. For the case in which the jobs with shorter lifetimes have longer service times, we observed that the optimal policy generally has a complex structure that might depend on the type and number of jobs available. For this case, we provide partial characterizations of the optimal policy and obtain sufficient conditions under which a state-independent policy is optimal. Furthermore, we develop two state-dependent heuristic policies, and by means of a numerical study, we show that these heuristics perform well, especially when jobs abandon the system at a relatively faster rate when compared to service rates. Based on our analytical and numerical results, we develop several insights on patient triage in the immediate aftermath of a mass casualty event. For example, we conclude that in a worst-case scenario, where medical resources are overwhelmed with a large number of casualties who need immediate attention, it is crucial to implement state-dependent policies such as the heuristic policies proposed in this article.

In this article we investigate less restrictive conditions on the model parameters that enable one to establish the likelihood ratio ordering of one generalized order statistic by conditioning on the right tail of another lower-indexed generalized order statistic. One application of the main results is also presented.

We derive a simple recursion to compute moments of arbitrary order of the duration of busy periods of MX/G/1/n systems starting with an arbitrary number of customers in the system.

We consider the virtual queuing time (vqt, also known as work-in-system, or virtual-delay) process in an M/G/s queue with impatient customers. We focus on the vqt-based balking model and relate it to reneging behavior of impatient customers in terms of the steady-state distribution of the vqt process. We construct a single-server system, analyze its operating characteristics, and use them to approximate the multiserver system. We give both analytical results and numerical examples. We conduct simulation to assess the accuracy of the approximation.

The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y defined by a weighted lattice polynomial of (lattice-valued) random variables is considered in general and in some special cases. The central object of interest is the cumulative distribution function of Y. In particular, numerous results are obtained for lattice polynomials and weighted lattice polynomials in the case of independent arguments and in general. For the general case, the technique consists in considering the joint probability generating function of “indicator” variables. A connection is studied between Y and order statistics of the set of arguments.

Recently, Belzunce, Ortega, Pellerey, and Ruiz [3] have obtained stochastic comparisons in increasing componentwise convex order sense for vectors of random sums when the summands and number of summands depend on a common random environment, which prove how the dependence among the random environmental parameters influences the variability of vectors of random sums. The main results presented here generalize the results in Belzunce et al. [3] by considering vectors of parameters instead of a couple of parameters and the increasing directionally convex order. Results on stochastic directional convexity of families of random sums under appropriate conditions on the families of summands and number of summands are obtained, which lead to the convex comparisons between random sums mentioned earlier. Different applications in actuarial science, reliability, and population growth are also provided to illustrate the main results.

The question of how long to run a discrete event simulation before data collection starts is an important issue when estimating steady-state performance measures such as average queue lengths. By using experiments based on numerical (nonsimulation) methods published elsewhere, we shed light on this question. Our experiments indicate that no initialization phase should be used when starting in state with a reasonable high equilibrium probability. Delaying data collection is only justified if the starting state is highly unlikely, and data collection should start as soon as a system enters a state with reasonably high probability.

This article derives the transient behavior of the stochastic process X(t) for which in earlier articles it was proven that for α<1, the process (X(t))1/(1−α) (approximately, under low drop probability or ECN marking probability) describes the behavior of the congestion windows in certain transport protocols in the so-called TCP paradigm. The transient distribution is found explicitly and is particularly transparent for moments like E[(X(t))k |X(0)]. The purpose of this article is to be part of the mathematical foundation when comparing the many protocols in the TCP paradigm.

In our article [3] we have found a gap in the middle of the proof of Theorem 3.2. Therefore, we do not know whether Theorem 3.2 is true for the reverse hazard rate order. However, we could prove the following weaker result for the stochastic order.