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Stabilizing performance in a single-server queue with time-varying arrival rate (2014).
| Content Provider | CiteSeerX |
|---|---|
| Author | Whitt, Ward |
| Abstract | We consider a general Gt/Gt/1 single-server queue with unlimited waiting space and a time-varying arrival rate, where the the service rate at each time is subject to control. We study the rate-matching control, where the the service rate is made proportional to the arrival rate. We show that the model with the rate-matching control can be regarded as a deterministic time transformation of a stationary G/G/1 model, so that the queue length distribution is stabilized as time evolves. However, the time-varying virtual waiting time is not stabilized. We show that the time-varying expected virtual waiting time with the rate-matching service-rate control becomes inversely proportional to the arrival rate in a heavy-traffic limit. We also show that no control that stabilizes the queue length asymptotically in heavy-traffic can also stabilize the virtual waiting time. Then we consider two square-root service-rate controls. We show that these alternative square-root service-rate controls stabilize the waiting time when the arrival rate changes very slowly relative to the average service time, so that a pointwise stationary approximation is appropriate. |
| File Format | |
| Publisher Date | 2014-01-01 |
| Access Restriction | Open |
| Subject Keyword | Single-server Queue Time-varying Arrival Rate Virtual Waiting Time Service Rate Arrival Rate Rate-matching Control Queue Length Distribution Time-varying Virtual Waiting Time Square-root Service-rate Control General Gt Gt Time Evolves Alternative Square-root Service-rate Control Queue Length Rate-matching Service-rate Control Deterministic Time Transformation Waiting Time Heavy-traffic Limit Pointwise Stationary Approximation Arrival Rate Change Average Service Time |
| Content Type | Text |
