Servicing Impatient Tasks That Have Uncertain Outcomes

Gaver, Donald P.; Jacobs, Patricia A.

doi:10.21236/ada370729

Cited by 7 publications

(9 citation statements)

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“…The strong performance of π SPI notwithstanding, its development via (8) and (9) is computationally prohibitive other than for small problems and special cases. In light of this computational intractability we proceed as follows: we shall develop an approximation V (1) …”

Section: Heuristic Policy Development-approximate Policy Improvement mentioning

confidence: 99%

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An approximate dynamic programing approach to the development of heuristics for the scheduling of impatient jobs in a clearing system

Liu

Glazebrook

2010

Naval Research Logistics

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A single server is faced with a collection of jobs of varying duration and urgency. Each job has a random lifetime during which it is available for nonpreemptive service. Should a job's lifetime expire before its service begins then it is lost from the system unserved. The goal is to schedule the jobs for service to maximize the expected number served to completion. Two heuristics have been proposed in the literature. One (labeled π S ) operates a static priority among the job classes and works well in a "no premature job loss" limit, whereas the second (π M ) is a myopic heuristic which works well when lifetimes are short. Both can exhibit poor performance for problems at some distance from the regimes for which they were designed. We develop a robustly good heuristic by an approximative approach to the application of a policy improvement step to the asymptotically optimal heuristic π S , in which we use a fluid model to obtain an approximation for the value function of π S . The performance of the proposed heuristic is investigated in an extensive numerical study.

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Section: Heuristic Policy Development-approximate Policy Improvement mentioning

confidence: 99%

“…Gaver and Jacobs [8] have argued the importance of incorporating job/customer impatience into service system models. They cite call center where customers will hang up if they are required to wait excessively for service and military scenarios in which enemy targets may move out of reach if not dealt with promptly.…”

Section: Introductionmentioning

confidence: 99%

An approximate dynamic programing approach to the development of heuristics for the scheduling of impatient jobs in a clearing system

Liu

Glazebrook

2010

Naval Research Logistics

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“…Assume defection during service is not observable. It is shown in Gaver et al (2000) that a good approximation to the long-run probability that successful service is achieved is…”

Section: A Self-thinning Approximation For An M/g/1 Model Of Success mentioning

confidence: 99%

“…Assume defection during service is not observable. It is shown in Gaver et al (2000) that a good approximation to the long-run probability that successful service is achieved is114where ( ) ( ) Suppose task service times have a distribution F S but service completion and task loss during service are not observable; then an approximation to the probability of successful task completion for a task that enters service is where the constant p represents the maximum probability of success, achieved as τ→∞; α is a scale, and β a shape parameter, both positive; if p<1, F S is a defective distribution.The exponent in the exponential function is unity (1) when α=τ, when the success probability becomesor about one-third of the maximum possible, and this independently of β. For τ<α the exponent increases rapidly as β increases; likewise, it decreases rapidly for τ>α with increasing p, representing threshold behavior at τ=α.…”

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confidence: 99%

Modeling and Analysis of Uncertain Time-Critical Tasking Problems (UTCTP)

Gaver¹,

Jr.²,

A.³

et al. 2003

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The ProblemConsider modeling and operational analysis of a generic asymmetrical service-system situation in which (a) Red agents, such as, military or facility-destructive hostile threats, arrive according to some partially known and possibly changing pattern in time and space; and (b) Reds have effectively limited unknown deadlines, or times of availability for Blue service, i.e. detection, classification, and attack in a military setting. Cases of known deadlines are important and somewhat analogous; see Lehoczky (1996Lehoczky ( , 1997aLehoczky ( , 1997b and Doytchinov et al. (2001).Think of the Reds as presenting tasks to be performed, or to be subjects of service. In a military context Reds may be perceived enemy targets, but in a medical emergency room setting they're arriving casualties. In a call center they are requests for information;see Becker et al (2000). In a Homeland Security (HLS) scenario a Red may be a container ship approaching a port, or a truck approaching a border, either possibly carrying explosives or chemical-biological offensive agents. We consider the Blue problem of processing such Red tasks effectively and efficiently under time constraints and limited information, hence the necessity to control the amount of service given. 2Appropriate service effort typically differs between task types; it may not always be completely provided, and may be partial and incomplete, owing to deficiency of time, information or resources. In general, task service is by a Blue force of task-server agents also of various types, possibly varying in number and organization, and at different locations, but which attempt to share information and the service burden. Such complex agent systems are considered elsewhere, using insights provided in this report. The Blue military objective is to successfully service as many tasks as possible rather than to minimize queues, while hostile Reds attempt to avoid "service," at least until they can accomplish their purpose, often to damage Blue. The models presented and analyzed suggest Blue force requirements and capability combinations for confronting specified challenges with acceptable success rates.To summarize, such service system issues arise ubiquitously in military operations of all kinds, as well as in Homeland Security (HLS) and in military force protection, emergency management situations, and many natural hazard response scenarios, such as after earthquakes or tidal waves. They also occur in call center design and operation, 3 wherein specialized operators are made available to assist users of new software issues (see Becker et al. (2000)).The plan of this paper is as follows. In Section 2 we describe a simple version of the basic problem: A single-type Red task arrival stream confronts a single Blue server that can process just one Red task at a time; success probability is related to allocated processing time, but is considered fixed/constant for a given selected processing mode.The Red tasks each have randomly limited availability time for processing, so i...

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“…This is our main object of study. In addition to the above, these models also enable us to consider scheduling problems in which tasks are impatient and may leave the system while awaiting processing (see Gaver and Jacobs [4]).…”

Section: Introductionmentioning

confidence: 99%

An index policy for a stochastic scheduling model with improving/deteriorating jobs

Glazebrook

Mitchell

2002

Naval Research Logistics

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Abstract:We consider stochastic scheduling models which have the natural character that jobs improve while being processed, but deteriorate (and may possibly leave the system altogether) while processing is diverted elsewhere. Such restless bandit problems are shown to be indexable in the sense of Whittle. A numerical study which elucidates the strong performance of the resulting index policy is complemented by a theoretical study which demonstrates the optimality of the index policy under given conditions and which develops performance guarantees for the index heuristic more generally.

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Servicing Impatient Tasks That Have Uncertain Outcomes

Cited by 7 publications

References 7 publications

An approximate dynamic programing approach to the development of heuristics for the scheduling of impatient jobs in a clearing system

An approximate dynamic programing approach to the development of heuristics for the scheduling of impatient jobs in a clearing system

Modeling and Analysis of Uncertain Time-Critical Tasking Problems (UTCTP)

An index policy for a stochastic scheduling model with improving/deteriorating jobs

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