Reneging from Processor Sharing Systems and Random Queues

Abstract
In a memoryless processor sharing system and in a memoryless random queue, both with some cost structure, it is shown that there exists an ε-Nash equilibrium symmetric reneging strategy which is Markovian and stationary with respect to the queue length and which is of the following (N*, θ*, η(ε)) form: (i) stay in the system when the queue size is smaller than some specified critical level N*; (ii) randomly renege with constant specified rate θ* when the queue size is N*; (iii) randomly renege with large enough rate ηn(ε) when the queue size is n with n>N*. Moreover, for all n with n>N*, limε→ 0ηn(ε)=∞. On the other hand, N* and θ* are not functions of ε and they depend only on the parameters defining the system. Finally, a stationary and Markovian symmetric Nash equilibrium strategy does not exist.

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