Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
A critically loaded multiclass Erlang loss system
Queueing Systems: Theory and Applications
Diffusion Approximations for Some Multiclass Queueing Networks with FIFO Service Disciplines
Mathematics of Operations Research
A heavy-traffic analysis of a closed queueing system with a GI/\infty service center
Queueing Systems: Theory and Applications
A critically loaded multirate link with trunk reservation
Queueing Systems: Theory and Applications
Strong approximations for Markovian service networks
Queueing Systems: Theory and Applications
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Capacity Management in Rental Businesses with Two Customer Bases
Operations Research
Usage Restriction and Subscription Services: Operational Benefits with Rational Users
Manufacturing & Service Operations Management
Dimensioning Large-Scale Membership Services
Operations Research
State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems
Mathematics of Operations Research
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We study a multiserver loss system with two kinds of customers: subscribers and infrequent users. We model the infrequent users' requests for service by a Poisson process. However, noting that the Poisson process is unable to capture repeated interactions as well as retrials, we propose a Markovian on-off-hold model for the subscribers' requests for service that takes into account retrials by subscribers denied service. We analyze this system in an asymptotic regime where the number of subscribers and the arrival rate of the Poisson stream, and consequently the number of servers, grow without bound. In this regime, we identify and prove convergence to diffusion limits for the system. We also prove the convergence of the invariant distributions to the invariant distribution of the limiting diffusions.