How Tolls Redistribute Customer Benefits in a M/M/1 Queuing System.
STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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In a FIFO MM1 queuing system an arriving customer chooses to enter the system if his reward for completing service is not less than a constant entrance toll plus expected waiting charge accumulated at a constant rate. Customers are partitioned into K classes according to their rewards. The long run average benefit reward minus waiting charge per arriving customer is computed for each class. Although a constant toll is fixed for all entering customers regardless of class or state of the system, the value of the toll can profoundly impact each classes long run average benefit per arriving customer. When the value of the toll is increased, the change in benefit per arriving customer is investigated for each customer class. These changes are a monotone increasing function of customer reward. Thus a toll increase is most valuable for those customers who obtain the highest reward from service completion. Results obtained assume that all rewards and tolls can be expressed as an integer multiple of a customers expected cost of waiting through his own service, and tolls are not subtracted in computing a customers benefit from entering the system. Author
- Numerical Mathematics
- Operations Research