Reneging from processor sharing systems and random queues
Mathematics of Operations Research
Optimal decentralized flow control of Markovian queueing networks with multiple controllers
Performance Evaluation
Competitive routing in multiuser communication networks
IEEE/ACM Transactions on Networking (TON)
On the existence of equilibria in noncooperative optimal flow control
Journal of the ACM (JACM)
Virtual path bandwidth allocation in multiuser networks
IEEE/ACM Transactions on Networking (TON)
A model for rational abandonments from invisible queues
Queueing Systems: Theory and Applications
Individual Equilibrium and Learning in Processor Sharing Systems
Operations Research
User equilibria for a parallel queueing system with state dependent routing
Queueing Systems: Theory and Applications
Monotonicity properties of user equilibrium policies for parallel batch systems
Queueing Systems: Theory and Applications
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We consider a service system where individual users share a common resource, modeled as a processor-sharing queue. Arriving users observe the current load in the system, and should decide whether to join it or not. The motivation for this model is based, in part, on best-effort service classes in computer communication networks. This decision problem is modeled as a noncooperative dynamic game between the users, where each user will enter the system only if its expected service time (given the system description and policies of subsequent users) is not larger than its quality of service (QoS) requirement. The present work generalizes previous results by Altman and Shimkin (1998), where all users were assumed identical in terms of their QoS requirements and decision policies; here we allow heterogeneous requirements, hence different policies. The main result is the existence and uniqueness of the equilibrium point in this system, which specifies a unique threshold policy for each user type. Computation of the equilibrium thresholds are briefly discussed, as well as dynamic learning schemes which motivate the Nash equilibrium solution for this system.