Risk-sensitive optimal control of queues
Author(s)Singh, Rahul; Modiano, Eytan H
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We consider the problem of designing risk-sensitive optimal control policies for scheduling packet transmissions in a stochastic wireless network. A single client is connected to an access point (AP) through a wireless channel. Packet transmission incurs a cost C, while packet delivery yields a reward of R units. The client maintains a finite buffer of size B, and a penalty of L units is imposed upon packet loss which occurs due to buffer overflow. We show that the risk-sensitive optimal control policy for such a simple set-up is of threshold type, i.e., it is optimal to carry out packet transmissions only when Q(t), i.e., the queue length at time t exceeds a certain threshold t. It is also shown that the value of the threshold t increases upon increasing the cost per unit packet transmission C. Furthermore, it is also shown that a threshold policy with threshold equal to t is optimal for a set of problems in which cost C lies within an interval [Cl, Cu]. Equations that need to be solved in order to obtain C¡, Cu are also provided.
DepartmentMassachusetts Institute of Technology. Laboratory for Information and Decision Systems; Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
2017 IEEE 56th Annual Conference on Decision and Control (CDC)
Institute of Electrical and Electronics Engineers (IEEE)
Singh, Rahul, Xueying Guo and Eytan Modiano. “Risk-sensitive optimal control of queues.” Paper presented at the 2017 IEEE 56th Annual Conference on Decision and Control (CDC) Conference, Melbourne, VIC, Australia, 12-15 Dec 2017, © 2017, IEEE The Author(s)