Scheduling In Multiclass Queueing System With Decaying Rewards

Some multiclass queuing systems have decaying customer rewards with respect to delayed service, such as medical triage system and perishable goods distribution system. Both decaying rewards and multiclass customers exist in these queuing systems, called decaying multiclass system. Research of decaying multiclass system stands in the cross area of Berth-Death Process, Earliness/Tardiness Scheduling and Multiclass Queuing, and the system is basically different from concepts of impatient customer and deteriorating job in existing literatures. This thesis investigates general characteristics and common decision-making model of decaying multiclass system, by the example of but not limited in medical triage system.The research is organized as follows. First, emergency medicine and operations research theories are applied into specific medical resource scheduling system. After literature review and typical case analysis, we define the post-disaster medicine scheduling system, in which scheduling problems considering multi-area, multi-category and multi-casualty are described respectively. Next, derived from work on medical resource scheduling system, we propose three general optimization problems in decaying multiclass system:scheduling among customer groups, scheduling among customer categories and scheduling among customers. Programming theory, Markov decision process and flexible job shop model are employed to develop solution of problems. Finally, numerical experiments are executed to validate reliability and efficiency of proposed models and algorithms, which create value when applied in many specific fields. Following steps above, we investigate decision making model of scheduling in decaying multiclass system. The details are as follows:(1) Scheduling problem of customer groups is derived from multi-area scheduling in medical resource scheduling system. A customer group is a set of customers, which are divided into several categories, and each category has independent decaying reward function. The customer categories are abstract of affected areas in disaster medical relief. Scheduling model of customer groups makesdecision to minimize system loss between current decision epoch and the next epoch, according to customer groups'numbers of customers, fixed servers, dispatchable servers, and distances between groups and save points as well. With primitive and statistical data of Wenchuan earthquake in emergency medicine literature, we execute numerical simulation. The result shows that proposed scheduling model can improve relief performance in disaster medical relief practice, better than existing subjective decision approaches including severity first strategy and distance first strategy.(2) Scheduling problem of customer categories is derived from multi-category scheduling in medical resource scheduling system. A customer category is a set of customers those follows same decaying reward distribution. Scheduling model among categories, established based on operations research and survival analysis theories, proposes a dynamic policy to determine scheduling solution according to number of customers in categories, service time distribution, and reward decaying rate. The policy dynamically maximizes system reward till termination of system. Numerical experiments are implemented under three conditions of linear reward function, general reward function and triage treatment respectively. The experiments evaluate proposed policy, named LE, compared with baseline policies such as R(t)r?, SEST and TCF. The result shows that LE achieves more total system reward than the other policies. Besides test efficiency and reliability, sensitivity analysis is executed on LE policy.(3) Scheduling problem of customer individuals is derived from multi-casualty scheduling in medical resource scheduling system. The decision model adopts Flexible job shop model and proposes a service scheduling approach, considering service time and reward of each individual. Individual's scheduling approach is a kind of dynamic genetic algorithm, allowing for disturbance of uncertain events.Therefore the approach is robust and good at global searching. Numerical experiments are implemented with data of natural disasters. Besides validate reliability and efficiency of the approach, results of experiments show that decision based on individuals makes more reward than that based on categories.This thesis studies common features and scheduling models of decaying multiclass system. In the theoretical level, the work expands research scope of queuing and scheduling theory. In the application level, potential work may apply the work into specific domains, and it could support decision maker to maximize efficiency of resource and minimize social loss.