Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-13T05:48:03.024Z Has data issue: false hasContentIssue false
  • English
  • Français

SCHEDULING IMPATIENT JOBS IN A CLEARING SYSTEM WITH INSIGHTS ON PATIENT TRIAGE IN MASS CASUALTY INCIDENTS

Published online by Cambridge University Press:  27 May 2008

Nilay Tanik Argon ,
Serhan Ziya  and
Rhonda Righter
Nilay Tanik Argon
Affiliation:
Department of Statistics and Operations ResearchUniversity of North CarolinaChapel Hill, NC 27599-3180 E-mail: nilay@email.unc.edu; ziya@email.unc.edu
Serhan Ziya
Affiliation:
Department of Statistics and Operations ResearchUniversity of North CarolinaChapel Hill, NC 27599-3180 E-mail: nilay@email.unc.edu; ziya@email.unc.edu
Rhonda Righter
Affiliation:
Department of Industrial Engineering and Operations ResearchUniversity of CaliforniaBerkeley, CA 94720-1777 E-mail: rrighter@ieor.berkeley.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 3 , July 2008 , pp. 301 - 332
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Arnold, J.L., Tsai, M.-C., Halpern, P., Smithline, H., Stok, E. & Ersoy, G. (2004). Mass-casualty, terrorist bombings: Epidemiological outcomes, resource utilization, and time course of emergency needs (Part I). Prehospital and Disaster Medicine 18(3): 220–234.CrossRefGoogle Scholar
2Bae, J., Kim, S. & Lee, E.Y. (2001). The virtual waiting time of M/G/1 queue with impatient customers. Queueing Systems 38: 485–494.CrossRefGoogle Scholar
3Bhattacharya, P.P. & Ephremides, A. (1989). Optimal scheduling with strict deadlines. IEEE Transactions on Automatic Control 34(7): 721–728.CrossRefGoogle Scholar
4Bhattacharya, P.P. & Ephremides, A. (1991). Optimal allocation of a server between two queues with due times. IEEE Transactions on Automatic Control 36(12): 1417–1423.CrossRefGoogle Scholar
5Boxma, O.J. & Forst, F.G. (1986). Minimizing the expected weighted number of tardy jobs in stochastic flow shops. Operations Research Letters 5(3): 119–126.CrossRefGoogle Scholar
6Brandt, A. & Brandt, M. (2002). Asymptotic results and a Markovian appproximation for the M(n)/M(n)/s + GI system. Queueing Systems 41: 73–94.CrossRefGoogle Scholar
7Brandt, A. & Brandt, M. (2004). On the two-class M/M/1 system under preemptive resume and impatience of the prioritized customers. Queueing Systems 47: 147–168.CrossRefGoogle Scholar
8Choi, B.D., Kim, B. & Chung, J. (2001). M/M/1 queue with impatient customers of higher priority. Queueing Systems 38: 49–66.CrossRefGoogle Scholar
9Coffman, E.G., Flatto, L., Garey, M.R. & Weber, R.R. (1987). Minimizing expected makespan on uniform processor systems. Advances in Applied Probability 19: 177–201.CrossRefGoogle Scholar
10Doytchinov, B., Lehoczky, J. & Shreve, S. (2001). Real-time queues in heavy traffic with earliest-deadline-first queue discipline. Annals of Applied Probability 11(2): 332–378.CrossRefGoogle Scholar
11Emmons, H. & Pinedo, M. (1990). Scheduling stochastic jobs with due dates on parallel machines. European Journal of Operational Research 47(1): 49–55.CrossRefGoogle Scholar
12Frykberg, E.R. (2002). Medical management of disasters and mass casualties from terrorist bombings: How can we cope? The Journal of Trauma 53(2): 201–212.CrossRefGoogle ScholarPubMed
13Glazebrook, K.D. (1983). Stochastic scheduling with due dates. International Journal of Systems Science 14: 1259–1271.CrossRefGoogle Scholar
14Glazebrook, K.D., Ansell, P.S., Dunn, R.T. & Lumley, R.R. (2004). On the optimal allocation of service to impatient tasks. Journal of Applied Probability 41(1): 51–72.CrossRefGoogle Scholar
15Hougaard, P. (2000). Analysis of multivariate survival data New York: Springer-Verlag.CrossRefGoogle Scholar
16Jang, W. & Klein, C.M. (2002). Minimizing the expected number of tardy jobs when processing times are normally distributed. Operations Research Letters 30: 100–106.CrossRefGoogle Scholar
17Jiang, Z., Lewis, T.G. & Colin, J.-Y. (1996). Scheduling hard real-time constrained periodic tasks on multiple processors. Journal of Systems and Software 19: 102–118.Google Scholar
18Levi, L., Michaelson, M., Admi, H., Bregman, D. & Bar-Nahor, R. (2003). National strategy for mass casualty situations and its effects on the hospital. Prehospital and Disaster Medicine 17(1): 12–17.CrossRefGoogle Scholar
19Nocera, A. & Garner, A. (1999). An Australian Mass Casualty Incident triage system for the future based upon triage mistakes of the past: The Homebush Triage Standard. Australian and New Zealand Journal of Surgery 69: 603–608.CrossRefGoogle ScholarPubMed
20Panwar, S.S., Towsley, D. & Wolf, J.K. (1988). Optimal scheduling policies for a class of queues with customer deadlines to the beginning of service. Journal of the Association for Computing Machinery 35(4): 832–844.CrossRefGoogle Scholar
21Peleg, K., Aharonson-Daniel, L., Michael, M., Shapira, S.C. & the Israel Trauma Group. (2003). Patterns of injury in hospitalized terrorist victims. American Journal of Emergency Medicine 21(4): 258–262.CrossRefGoogle ScholarPubMed
22Pinedo, M. (1983). Stochastic Scheduling with release dates and due dates. Operations Research 31(3): 559–572.CrossRefGoogle Scholar
23Righter, R. (1994). Scheduling. Shaked, I.M. & Shanthikumar, J.G., (eds.) Stochastic orders New York: Academic Press, pp. 381–432.Google Scholar
24Righter, R. (1988). Job scheduling to minimize weighted flowtime on uniform processors. Systems and Control Letters 10: 211–216.CrossRefGoogle Scholar
25Righter, R. (2000). Expulsion and scheduling control for multiclass queues with heterogenous servers. Queueing Systems 34: 289–300.CrossRefGoogle Scholar
26Rund, D.A. & Rausch, T.S. (1981). Triage St. Louis, MO: C.V. Mosby.Google Scholar
27Van Mieghem, J. (1995). Dynamic scheduling with convex delay costs: the generalized cμ rule. Annals of Applied Probability 5(3): 808–833.CrossRefGoogle Scholar
28Van Mieghem, J. (2003). Due date scheduling: asymptotic optimality of generalized longest queue and generalized largest delay rules. Operations Research 51(1): 113–122.CrossRefGoogle Scholar
29Ward, A.R. & Glynn, P.W. (2003). A diffusion approximation for a Markovian queue with reneging. Queueing Systems 43: 103–128.CrossRefGoogle Scholar
30Ward, A.R. & Kumar, S. (2008). Asymptotically optimal admission control of a queue with impatient customers. Mathematics of Operations Research 33: 167–202.CrossRefGoogle Scholar
31Weber, R.R., Varaiya, P. & Walrand, J. (1986). Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flow time. Journal of Applied Probability 23: 841–847.CrossRefGoogle Scholar
32Weiss, G. & Pinedo, M. (1980). Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions. Journal of Applied Probability 17: 187–202.CrossRefGoogle Scholar
33Xu, S.H. (1994). A duality approach to admission and scheduling control of queues. Queueing Systems 18: 273–300.CrossRefGoogle Scholar
34Zhao, Z.-X., Panwar, S.S. & Towsley, D. (1991). Queueing performance with impatient customers. Proceedings of IEEE INFOCOM’91 1: 400–409.Google Scholar