54 research outputs found
Fairness in overloaded parallel queues
Maximizing throughput for heterogeneous parallel server queues has received
quite a bit of attention from the research community and the stability region
for such systems is well understood. However, many real-world systems have
periods where they are temporarily overloaded. Under such scenarios, the
unstable queues often starve limited resources. This work examines what happens
during periods of temporary overload. Specifically, we look at how to fairly
distribute stress. We explore the dynamics of the queue workloads under the
MaxWeight scheduling policy during long periods of stress and discuss how to
tune this policy in order to achieve a target fairness ratio across these
workloads
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
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
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