2013/01/20 by Ohad Perry, Ward Whitt, Perry, Ohad +1
Business, Management and Accounting · Computer Science · Psychology · #60K25 #90B22 #Advanced Queuing Theory Analysis #FOS: Mathematics #Mental Health Research Topics #Network Traffic and Congestion Control #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1301.4713
openalex publication_date 2013/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an automatic overload control for two large service systems\nmodeled as multi-server queues, such as call centers. We assume that the two\nsystems are designed to operate independently, but want to help each other\nrespond to unexpected overloads. The proposed overload control automatically\nactivates sharing (sending some customers from one system to the other) once a\nratio of the queue lengths in the two systems crosses an activation threshold\n(with ratio and activation threshold parameters for each direction). To prevent\nharmful sharing, sharing is allowed in only one direction at any time. In this\npaper, we are primarily concerned with ensuring that the system recovers\nrapidly after the overload is over, either (i) because the two systems return\nto normal loading or (ii) because the direction of the overload suddenly shifts\nin the opposite direction. To achieve rapid recovery, we introduce lower\nthresholds for the queue ratios, below which one-way sharing is released. As a\nbasis for studying the complex dynamics, we develop a new six-dimensional fluid\napproximation for a system with time-varying arrival rates, extending a\nprevious fluid approximation involving a stochastic averaging principle. We\nconduct simulations to confirm that the new algorithm is effective for\npredicting the system performance and choosing effective control parameters.\nThe simulation and the algorithm both show that the system can experience an\ninefficient nearly-periodic behavior, corresponding to an oscillating\nequilibrium (congestion collapse), if the sharing is strongly inefficient and\nthe control parameters are set inappropriately.\n