Redundant Queueing System with Hysteresis Backup Server Connection Strategy
We consider an unreliable queueing system which can be used for modeling a broadband hybrid communication channel consisting FSO (Free Space Optics) channel and radio wave channel. The radio channel is backup and is connected when the optical channel is not available. In order to save energy, a hysteresis strategy for connecting a backup channel is used. This strategy is given by two thresholds: \(j_1\) and \(j_2, j_1\le j_2.\) If the main channel fails, the backup channel connects to information transmission if the number i of customers in the system is such that \(i>j_2.\) If during backup channel operation the number of customers in the system becomes such that \(i\le j_1,\) then the backup channel is disabled and the current customer continues to be serviced at the main server. If at some point in time the number i of customers in the system becomes such that \(j_1<i\le j_2,\) then the system works in the mode in which it worked until that time. We describe the system operation by two-dimensional Markov chain, calculate the steady state distribution and the main performance characteristics of the system. We introduce the cost function and present the example of numerical optimisation consisting in choosing the threshold values minimizing the cost function.
KeywordsUnreliable queueing system Backup server Hysteresis strategy Steady state distribution Performance characteristics Cost function Optimisation problem
This work has been financially supported by the joint grant of Belarusian Republican Foundation for Fundamental Research (No F18R-136) and Russian Foundation for Fundamental Research (No 18-57-00002).
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