We consider two types of queues with workload-dependent arrival rate and service speed. Our study is motivated by queueing scenarios where the arrival rate and/or speed of the server depends on the amount of work present, like production systems and the Internet. First, in the M/G/1 case, we compare the steady-state distribution of the workload (both at arbitrary epochs and at arrival instants)...

In this paper, analysis of variance and standard deviation interdependent stochastic feedback arrival rate single server with service are considered. The steady-state solution system characteristics derived for model. effect the nodal parameters on is established using Maple software analytical results numerically illustrated relevant conclusions presented.

This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the system are derived, based on stochastic monotonicity and marginal drift properties of multiclass birth and death processes. These conditions yield a sharp ch...

We consider a class of general Gt/Gt/1 single-server queues, including the Mt/Mt/1 queue, with unlimited waiting space, service in order of arrival, and a time-varying arrival rate, where the service rate at each time is subject to control. We study the rate-matching control, where the service rate is made proportional to the arrival rate. We show that the model with the rate-matching control c...

We consider a class of general Gt/Gt/1 single-server queues, including the Mt/Mt/1 queue, with unlimited waiting space, service in order of arrival and a time-varying arrival rate, where the the service rate at each time is subject to control. We study the rate-matching control, where the the service rate is made proportional to the arrival rate. We show that the model with the rate-matching co...

The arrival curve has been used as a powerful concept for deterministic service guarantee analysis in communication networks. Since many applications and networks do not require or provide deterministic service guarantees, stochastic service guarantee analysis is becoming increasingly important and has attracted a lot of research attention in recent years. For this, several probabilistic versio...

In this paper, we consider a variant of an M/M/c/c loss system with fluctuating server capacity. Given a set of primary inputs, such as arrival rate, service rate, and capacity fluctuation rate, we develop a detailed model using MRGP, such that blocking and dropping metrics can be calculated explicitly. To gain insight into performance implications of a stochastic capacity queue, we conduct an ...