On the optimal control of arrivals to a single queue with arbitrary feedback delay
We consider a problem of admission control to a single queue in discrete time. The controller has access to k -step old queue lengths only, where k can be arbitrary. The problem is motivated, in particular, by recent advances in high-speed networking ...
Extreme and high-level sojourns of the single server queue in heavy traffic
This study characterizes the behavior of large queue lengths in heavy traffic. We show that the distribution of the maximum queue length in a random time interval for a queueing systems in heavy traffic converges to a novel extreme value distribution. ...
Parallel simulation by multi-instruction, longest-path algorithms
This paper presents several basic algorithms for the parallel simulation of G/G/1 queueing systems and certain networks of such systems. The coverage includes systems subject to manufacturing or communication blocking, or to loss of customer due to ...
Two finite-difference methods for solving MAP(t)/PH(t)/1/K queueing models
In this paper two solution methods to the MAP(t)/PH(t)/1/K queueing model are introduced, one based on the Backwards Euler Method and the other on the Uniformization Method. Both methods use finite-differencing with a discretized, adaptive time-mesh to ...
Admission control of multi-class traffic with service priorities in high-speed networks
We consider a fluid model of a system that handles multiple classes of traffic. The delay and cell-loss requirements of the different classes of traffic are generally widely different and are achieved by assigning different buffers for different classes,...
Fluid approximations for a processor-sharing queue
In this paper a fluid approximation, also known as a functional strong law of large numbers (FSLLN) for a GI/G/1 queue under a processor-sharing service discipline is established and its properties are analysed. The fluid limit depends on the arrival ...
On a decomposition for infinite transition matrices
Heyman gives an interesting factorization of I-P , where P is the transition probability matrix for an ergodic Markov chain. We show that this factorization is valid if and only if the Markov chain is recurrent. Moreover, we provide a decomposition ...
Generalized model with repeated calls in case of extreme load
Recurrence formulas for finding any desired number of terms in the asymptotic expansion of basic stationary performance measures of a generalized full-available system with repeated calls into a power series of the intensity of primary calls as it tends ...
Analysis of a single server queue with semi-Markovian service interruption
In this paper we analyze a discrete-time single server queue where the service time equals one slot. The numbers of arrivals in each slot are assumed to be independent and identically distributed random variables. The service process is interrupted by a ...
The tightness in the ergodic analysis of regenerative queueing processes
The tightness of some queueing stochastic processes is proved and its role in an ergodic analysis is considered. It is proved that the residual service time process in an open Jackson-type network is tight. The same problem is solved for a closed ...
