ICATPN '02 Proceedings of the 23rd International Conference on Applications and Theory of Petri Nets
Multiclass Multiserver Threshold-Based Systems: A Study of Noninstantaneous Server Activation
IEEE Transactions on Parallel and Distributed Systems
Discrete-time bulk-service queue with two heterogeneous servers
Computers and Industrial Engineering
Finite capacity M/M/r queueing system with queue-dependent servers
Computers & Mathematics with Applications
Analysis of the busy period in threshold control system
Automation and Remote Control
Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems
Operations Research
Performance analysis of finite buffer queueing system with multiple heterogeneous servers
ICDCIT'10 Proceedings of the 6th international conference on Distributed Computing and Internet Technology
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A dynamic control policy known as "threshold queueing" is defined for scheduling customers from a Poisson source on a set of two exponential servers with dissimilar service rates. The slower server is invoked in response to instantaneous system loading as measured by the length of the queue of waiting customers. In a threshold queueing policy, a specific queue length is identified as a "threshold," beyond which the slower server is invoked. The slower server remains busy until it completes service on a customer and the queue length is less than its invocation threshold. Markov chain analysis is employed to analyze the performance of the threshold queueing policy and to develop optimality criteria. It is shown that probabilistic control is sub-optimal to minimize the mean number of customers in the system. An approximation to the optimum policy is analyzed which is computationally simple and suffices for most operational applications.