Olga V. Semenova

Performance analysis of the BMAP/G/1 queue with gated servicing and adaptive vacations

A queueing model of the BMAP/G/1 type with gated servicing and vacations depending on the state of the system is analysed. The queue stationary distributions at the instants of gate switching on and at arbitrary time as well as of a customer waiting time are computed. This model may prove useful for tuning the parameters of the adaptive polling mechanism applicable in the broadband wireless Wi-Fi and WiMax networks.

The power-series algorithm for two-queue polling system with impatient customers

Two-queue system with queue alternate exhaustive service and customerspsila impatience (stochastic time out) is considered. The switch-over times are assumed to be non-zero. The computation scheme of the power-series algorithm for the evaluation of the joint queue length distributions for the model under consideration is presented. Having the joint queue length distributions calculated, we can obtain the performance characteristics.

Approximate Method to Study M/G/1-Type Polling System with Adaptive Polling Mechanism

Abstract We investigate a polling model of a radio-cell of the broadband wireless IEEE 802.11 network. A radio-cell is assumed to work in the “data collection” regime. It is modeled by a polling system with N queues and a single server polling the queues in a cyclic adaptive order. Under adaptive scheme, the server (base station) skips (does not visit) the queues (subscriber stations) which were empty at their polling moments at the previous cycle that allows cutting expenses. In the paper, we present an iterative procedure for calculating the first and second moments of the waiting time in queues and provide numerical examples to compare theoretical results and ones obtained from simulation.

Optimal control of M/M/1 queueing system with constant retrial rate and non-reliable removable server

The paper is concerned with the optimal control with respect to N-policy of the M/M/1 queue with constant retrial rate and non-reliable removable server. According to the N-policy, the server can start service only when the number of customers in the system reaches level N (N ≥ 1). We perform a steady-state analysis of the corresponding continuous-time Markov chain and calculate optimal threshold level to minimize the longrun average losses given cost structure.

M|M|N Queueing System with Controlled Service Mode and Disaster

An M|M|N queueing system with identical servers and controlled mode, which is characterized by the parameter, “exponential distribution of service time,” is considered. The mode varies in accordance with a multithreshold strategy. The system is subjected to the action of catastrophic failures that induce the departure of all the customers from the system. An algorithm is developed for calculating the stationary state probability of the system and the performance characteristics with fixed control strategy. An optimal strategy is found numerically in a limited region of values of the threshold. Numerical examples are presented.

Redundant queuing system with unreliable servers

We consider a two-channel queuing system with unreliable servers which fail alternately for modeling of hybrid communication systems, which have a millimeter-wave (71-76 GHz, 81-86 GHz) radio channel as a backup communication channel. The stationary distribution of the system states and the most important performance characteristics were obtained.

The power-series algorithm for M/M/1-type polling system with impatient customers

We investigate a polling model for a radio-cell of the broadband wireless IEEE 802.11 DCF network. Polling system consists of N M/M/1-type queues with impatient customers. The switchover times are assumed to be non-zero. A customer has limited random waiting time and after the time expires the customer leaves the system unless its service has not been started. The computation scheme of the power-series algorithm for the evaluation of the joint queue length distributions for the model under consideration is presented. Having the joint queue length distributions calculated, we obtain the performance characteristics.

Method of Generating Functions for Performance Characteristic Analysis of the Polling Systems with Adaptive Polling and Gated Service

In the paper, we consider a polling system with a cyclic adaptive polling order. The server polls the queues in a cyclic way but skips (does not visit) those that were empty when polling them in the previous cycle. We apply the generating function method to derive first and second order moments of the stationary state distribution of the queue length at the polling moments that allows calculating the mean delay in queues. Also we provide numerical results.

State Reduction in Analysis of a Tandem Queueing System with Correlated Arrivals

Tandem queueing systems often arise in wireless networks modeling. Queueing models are very suitable for network performance evaluation but the system complexity exponential growth (or state space explosion) could make the analysis barely feasible. The paper presents a comparative study of various methods of a state space reduction for markovian arrival processes (MAP) and phase-type distributions (PH) applied to tandem queueing systems. The applied methods include nonlinear optimization, EM-algorithm and linear minimization. While most of the described algorithms are well-studied, a number of issues arises when applying them to a tandem system of a real wireless network. Particularly, it is shown that while all the algorithms could be applied to tandems with a small number of queues, bigger tandems require additional effort to get the appropriable results. Nevertheless, the results presented show that the departure MAPs reduction may help to solve the state space explosion problem.

Performance analysis of the queue with gated servicing and adaptive vacations

A queueing model of the BMAP/G/1 type with gated servicing and vacations depending on the state of the system is analysed. The queue stationary distributions at the instants of gate switching on and at arbitrary time as well as of a customer waiting time are computed. This model may prove useful for tuning the parameters of the adaptive polling mechanism applicable in the broadband wireless Wi-Fi and WiMax networks.