3 research outputs found
Convexity Properties and Comparative Statics for M/M/S Queues with Balking and Reneging
We use sample path arguments to derive convexity properties of an M/M/S queue with
impatient customers that balk and renege. First, assuming that the balking probability and
reneging rate are increasing and concave in the total number of customers in the system
(head-count), we prove that the expected head-count is convex decreasing in the capacity
(service rate). Second, with linear reneging and balking, we show that the expected lost sales
rate is convex decreasing in the capacity. Finally, we employ a sample-path sub-modularity
approach to comparative statics. That is, we employ sample path arguments to show how the
optimal capacity changes as we vary the parameters of customer demand and impatience.
We find that the optimal capacity increases in the demand rate and decreases with the
balking probability, but is not monotone in the reneging rate. This means, surprisingly, that
failure to account for customersâ reneging may result in over-investment in capacity. Finally,
we show that a seemingly minor change in system structure, customer commitment during
service, produces qualitatively different convexity properties and comparative statics.Operations Management Working Papers Serie