Recurrent events in queues with independent arrival intervals

Markovian Queues with Correlated Arrival Processes

In an attempt to examine the effect of dependencies in the arrival process on the steady state queue length process in single server queueing models with exponential service time distribution, four different models for the arrival process, each with marginally distributed exponential interarrivals to the queueing system, are considered. Two of these models are based upon the upper and lower bou...

Finite-Buffer Queues with Workload-Dependent Service and Arrival Rates

We consider M/G/1 queues with workload-dependent arrival rate, service speed, and restricted accessibility. The admittance of customers typically depends on the amount of work found upon arrival in addition to its own service requirement. Typical examples are the finite dam, systems with customer impatience and queues regulated by the complete rejection discipline. Our study is motivated by que...

Heavy-traffic limits for queues with periodic arrival processes

We establish conventional heavy-traffic limits for the number of customers in a Gt/GI/s queue with a periodic arrival process. We assume that the arrival counting process can be represented as the composition of a cumulative stochastic process that satisfies an FCLT and a deterministic cumulative rate function that is the integral of a periodic function. We establish three different heavy-traff...

Single retrial queues with service option on arrival

On Queues with Inter-Arrival Times Proportional to Service Times

We analyze a family of queueing systems where the interarrival time I n+1 between customers n and n + 1 depends on the service time B n of customer n. Speciically, we consider cases where the dependency between I n+1 and B n is a proportionality relation, and B n is an exponentially distributed random variable. Such dependencies arise in the context of packet-switched networks which use rate po...