Rhonda Righter

Distributed simulation of discrete event systems

An overview of distributed simulation of discrete event systems and the issues associated with it. Alternative approaches for decomposing the simulation into tasks that can be run on separate processors are described, and the potential parallelism associated with certain kinds of decomposition is studied. Existing synchronization algorithms are discussed. An attempt is made throughout to show what decomposition approaches and synchronization algorithms may be appropriate depending on properties of the application and the multiprocessor architecture. Empirical and analytical performance studies are described, where available. >

Scheduling impatient jobs in a clearing system with insights on patient triage in mass casualty incidents

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.

Resource allocation in grid computing

Abstract Grid computing, in which a network of computers is integrated to create a very fast virtual computer, is becoming ever more prevalent. Examples include the TeraGrid and Planet-lab.org, as well as applications on the existing Internet that take advantage of unused computing and storage capacity of idle desktop machines, such as Kazaa, SETI@home, Climateprediction.net, and Einstein@home. Grid computing permits a network of computers to act as a very fast virtual computer. With many alternative computers available, each with varying extra capacity, and each of which may connect or disconnect from the grid at any time, it may make sense to send the same task to more than one computer. The application can then use the output of whichever computer finishes the task first. Thus, the important issue of the dynamic assignment of tasks to individual computers is complicated in grid computing by the option of assigning multiple copies of the same task to different computers. We show that under fairly mild and often reasonable conditions, maximizing task replication stochastically maximizes the number of task completions by any time. That is, it is better to do the same task on as many computers as possible, rather than assigning different tasks to individual computers. We show maximal task replication is optimal when tasks have identical size and processing times have a NWU (New Worse than Used; defined later) distribution. Computers may be heterogeneous and their speeds may vary randomly, as is the case in grid computing environments. We also show that maximal task replication, along with a cμ rule, stochastically maximizes the successful task completion process when task processing times are exponential and depend on both the task and computer, and tasks have different probabilities of completing successfully.

A Resource Allocation Problem in a Random Environment

We consider a resource allocation problem in which various parameters of the model change according to independent random environment Markov processes. There are a finite number of activities that each require a resource, and resources arrive according to a Poisson process. Both activities and resources have values associated with them and the return from allocating a resource to an activity is the product of the activity value and the resource value. Activity values are known ahead of time but the values of resources are independent random variables from a common distribution and are known only after the arrival of the resource. We wish to assign arriving resources to available activities so as to maximize our total expected return. It is assumed that either there is a single random deadline for all activities, which is the same as discounting the returns, or the activities have independent random deadlines. The model has applications to processor scheduling, selling of assets, and kidney allocation for transplant. We consider the effects on the structure of the optimal policy of allowing parameters to be determined by independent Markov processes. In particular, we permit the resource arrival rate, the activity values, the deadline rates, and the variability of the resource distribution to change. We give conditions under which the total optimal expected return is monotone in the states of the Markov processes. We also show that the total optimal return is increasing and convex in the activity values, decreasing and convex in the deadline rates, and increasing if the variability of the distribution of resource values is increasing.

Optimal dynamic assignment of customers to heterogeneous servers in parallel

The system under consideration comprises two classes of customers to be served by two stations, with parallel servers in each station. While class-1 customers can only receive service from station 1, class-2 customers can be served by either station. Arrival processes of customers form two mutually independent Poisson processes. The service time of a customer at either station is exponentially distributed with a common rate. A class- i customer, while present in the system, will incur a holding cost h i with h 1 ≥ h 2 . The objective is to dynamically assign customers to idle servers so that the expected discounted (or the long-run average) holding cost is minimized. We show that a class- j customer should be assigned to an idle server in station j , j = 1, 2, whenever possible, and a class-2 customer should be assigned to an idle server in station 1 only if (no class-1 customers are waiting, and) the length of queue 2 exceeds a critical number. Moreover, the critical number is monotonically increasing in the number of busy servers in station 1. The numerical results for some test cases are reported.

Extremal properties of the FIFO discipline in queueing networks

We show that using the FIFO service discipline at single server stations with ILR (increasing likelihood ratio) service time distributions in networks of monotone queues results in stochastically earlier departures throughout the network. The converse is true at stations with DLR (decreasing likelihood ratio) service time distributions. We use these results to establish the validity of the following comparisons: (i) The throughput of a closed network of FIFO single-server queues will be larger (smaller) when the service times are ILR (DLR) rather than exponential with the same means. (ii) The total stationary number of customers in an open network of FIFO single-server queues with Poisson external arrivals will be stochastically smaller (larger) when the service times are ILR (DLR) rather than exponential with the same means. We also give a surprising counterexample to show that although FIFO stochastically maximizes the number of departures by any time t from an isolated single-server queue with IHR (increasing hazard rate, which is weaker than ILR) service times, this is no longer true for networks of more than one queue. Thus the ILR assumption cannot be relaxed to IHR. Finally, we consider multiclass networks of exponential single-server queues, where the class of a customer at a particular station determines its service rate at that station, and show that serving the customer with the highest service rate (which is SEPT — shortest expected processing time first) results in stochastically earlier departures throughout the network, among all preemptive work-conserving policies. We also show that a cµ rule stochastically maximizes the number of non-defective service completions by any time t when there are random, agreeable, yields.

The Stochastic Sequential Assignment Problem With Random Deadlines

Resources are to be allocated sequentially to activities to maximize the total expected return, where the return from an allocation is the product of the value of the resource and the value of the activity. The set of activities and their values are given ahead of time, but the resources arrive according to a Poisson process and their values are independent random variables that are observed upon arrival. It is assumed that either there is a single random deadline for all activities, which is the same as discounting the returns, or the activities have independent random deadlines. The model has applications machine scheduling, packet switching, and kidney allocation for transplant. It is known that the optimal policy in the discounted case has a very simple form that does not depend on the activity values. We show that this is also true when the deadlines are independent and in this case the solution can expressed in terms of solutions to single activity models. These results also hold when there are batch arrivals of resources. The effects of pooling separate identical systems with a single activity into a combined system is investigated for both models. When activities have independent deadlines it is optimal to reject a resource in the combined system if and only if it is optimal to reject it in the single activity system. However, when returns are discounted, it is sometimes optimal to accept a resource in the combined system that would be rejected in the single activity system.

Task Assignment in a Heterogeneous Server Farm with Switching Delays and General Energy-Aware Cost Structure

Abstract We consider the task assignment problem to heterogeneous parallel servers with switching delay, where servers can be switched off to save energy. However, switching a server back on involves a constant server-specific delay. We will use one step of policy iteration from a starting policy such as Bernoulli splitting, in order to derive efficient task assignment (dispatching) policies that minimize the long-run average cost. To evaluate our starting policy, we first analyze a single work-conserving M / G / 1 queue with a switching delay and derive a value function with respect to a general cost structure. Our costs include energy related switching and processing costs, as well as general performance-related costs, such as costs associated with both means and variability of waiting time and sojourn time. The efficiency of our dispatching policies is illustrated with numerical examples.

Dynamic load balancing with flexible workers

We study the problem of dynamically allocating flexible workers to stations in tandem or serial manufacturing systems. Workers are trained to do a subset of consecutive tasks. We show that the optimal policy is often LBFS (last buffer first-served) or FBFS (first buffer first-served). These results generalize earlier results on the optimality of the pick-and-run, expedite, and bucket brigade-type policies. We also show that, for exponential processing times and general manufacturing networks, the optimal policy will tend to have several workers assigned to the same station.

Job scheduling to minimize expected weighted flowtime on uniform processors

Abstract We consider a sequencing problem in which there are n jobs to be processed nonpreemptively on m nonidentical processors. The processing time of the j- th processor is exponentially distributed with rate μ j , where μ 1 ⩾μ 2 ⩾⋯⩾μ m . Job i incurs a holding cost at rate c i per unit time while still in the system, where c 1 ⩾c 2 ⩾⋯⩾c n . We show that to minimize total expected holding costs (weighted flowtime), it is optimal to take the fastest (lowest indexed) available processor, say processor j , and assign job k to it if k>(Σ i j − 1 μ i )/μ j −j ⩾ k−1 . After each assignment the jobs are renumbered (so that job k+1 becomes job k , etc.), and the procedure is repeated with the next fastest available processor, etc. Note that the policy does not depend on the values of the holding costs c i . This result is a generalization of the result of Agrawala et al. (1984) for minimizing expected flowtime, i.e., minimizing total holding cost when the holding costs of all the jobs are the same. We give a simpler proof of the more general result.