Tien Van Do

The MMΣk=1KCPPk/GE/c/L G-queue with heterogeneous servers: Steady state solution and an application to performance evaluation

A new queue, referred to here as the HetSigma queue, in the Markovian framework, is proposed in order to model nodes in modern telecommunication networks. The queue has many of the necessary ingredients, such as joint (or individual) Markov modulation of the arrival and service processes, superposition of K CPP (compound Poisson process) streams of (positive) customer arrivals, and a CPP of negative customer arrival stream in each of the modulating phases, a multiserver with c non-identical (can also be identical) servers, GE (generalised exponential) service times in each of the modulating phases and a buffer of finite or infinite capacity. Thus, the model can accommodate correlations of the inter-arrival times (of batches), and geometric as well as non-geometric batch size distributions of customers in both arrivals and services. The use of negative customers can facilitate modelling server failures, packet losses, load balancing, channel impairment in wireless networks, and in many other applications. An exact and computationally efficient solution of this new queue for steady state probabilities and performance measures is developed and presented. A non-trivial application of the new queue to the performance evaluation of a wireless communication system is presented, along with numerical results, to illustrate the efficacy of the proposed method. The use of negative customers is also demonstrated. The new queue, perhaps with further evolution, has the potential to emerge as a generalised Markovian node model.

An initiative for a classified bibliography on G-networks

In the last two decades, researchers have really been embracing the idea of G-networks with negative arrivals and the relevant product form solution including nonlinear traffic equations, which is the unified model for queueing networks and neural networks. This paper reports the initiative to collect and classify a bibliography on G-networks.

An integrated analytical model for computation and comparison of the throughputs of the UMTS/HSDPA user equipment categories

A new queuing model is proposed for the performance evaluation of the High Speed Downlink Packet Access (HSDPA) protocol, with respect to a specified user, in UMTS networks. The model is based on the recently evolved MM ΣΚκ= CPPκGEcLG-queue1, in which the number of servers allocated to a specified user is subjected to vary according to the physical channel allocation policy. This queue is, essentially, an important variant of the so-called Sigma queuing model, and it is able to capture most of the features of HSDPA wireless communications, such as traffic-burstiness, channel fading, channel allocation policy, etc., in an integrated way. Numerical results for the performance of HSDPA with respect to a specified user are obtained, and different HSDPA user equipment categories are compared with respect to their computed model throughputs.

Performance modeling of an Apache Web server with a dynamic pool of service processes

In the current Internet the performance of service delivery crucially depends on the proper and efficient operation of Web servers. It is determined by their software architecture and characterized by the applied processing model.Here we consider the Unix software architecture of an Apache Web server with its non-threaded multi-processing module Prefork. We propose a tractable multi-server model to approximate the performance of the load-dependent dynamic behavior of Apache’s resource pool of available HTTP service processes, which has not been done before. Furthermore, we show that this Markovian queueing model can be solved by advanced matrix-geometric methods. Then the efficiently computed performance results of this analytic model are compared with measurements of a real Apache Web server. The outcome clearly indicates that our analytic model can very accurately predict the mean-value performance of Apache under the Prefork policy.

A new performability model for queueing and FDL-related burst loss in optical switching nodes

Optical packet and burst switching have been proposed for networks because of the increased demand for capacity to transport traffic generated by various applications at present and in future. In optical packet switching networks the payload and the header of a packet are conveyed in the same channel, while burst switching networks allow the separate transportation of the payload and the header of bursts. In this paper we propose a queueing model for an optical node with a number of wavelengths and a buffer made from Fiber Delay Loops (FDL). We also apply negative customers in the queueing model in order to account for the loss of bursts due to the limitation related to the FDL (i.e. bursts can stay in a FDL buffer only for a limited period of time). Numerical results based on the analytical model are compared to the results obtained by simulation of optical burst switching nodes with the FDL buffer and input traffic using packet traces from the Internet Traffic Archive, which shows the accuracy of the proposed model.

Performance Evaluation of the High Speed Downlink Packet Access in Communications Networks Based on High Altitude Platforms

In this paper, we provide a performance model and viable evaluation for the Adaptive Modulation and Coding (AMC) used in High Altitude Platforms (HAP) based HSDPA/UMTS telecommunication networks. We incorporate the HAP channel model into a new queueing model which is able to capture most of the features of wireless communications, such as traffic-burstiness, channel fading, channel allocation policy, etc., in an integrated way. In a case study we validate the model with the use of ns-2 simulator and also present numerical results to evaluate the impact of the HAP environment on the performance of HSDPA user terminal categories.

A new queueing model for spectrum renting in mobile cellular networks

Spectrum renting is an operation practice that can be applied to relieve the temporary capacity shortages of a specific service area in wireless cellular networks. However, works in the literature do not take into account the specific feature of the present wireless technology. That is, the separate blocks of user channels are defined in each frequency band in the current standards for public mobile cellular networks, and each block should be controlled by a single network operator. This paper is the first attempt to model the spectrum renting policies and the call admission control in a realistic way. The comparison between a queueing model and a simulation model confirms that the proposed queueing model incorporating exponentially distributed call durations can be used to evaluate the performance of mobile cellular networks with call holding times following the lognormal distribution as well. Numerical results show that the variants of the Fractional Guard Channel Policy provide an efficient tool to guarantee the grade of service of handover calls at the expense of increased blocking probability of fresh calls. Furthermore, only spectrum renting can be used to decrease the blocking probability of fresh calls without compromising the grade of service of handover calls.

An efficient method to compute the rate matrix for retrial queues with large number of servers

Abstract The approximate solution technique for the main M / M / c retrial queue based on the homogenization of the model employs a quasi-birth–death (QBD) process in which the maximum retrial rate is restricted above a certain level. This approximated continuous-time Markov chain (CTMC) can be solved by the matrix-geometric method, which involves the computation of the rate matrix R . This paper is motivated by two observations. Firstly, retrial queues for the performability analysis of telecommunication systems often involve the number of servers in the order of several hundreds of thousands. Secondly, there are no workable solutions till now for systems with such large number of servers, due to ill-conditioning or prohibitively large computation times. Our paper is the first to tackle the problem of large number of servers, very efficiently, in the homogenized M / M / c retrial queue which has paramount applications in networks. We present an efficient algorithm with the time complexity of only O ( c ) to compute the rate matrix R .

A Performance Model for Maintenance Tasks in an Environment of Virtualized Servers

This paper introduces the CPP/M/c model with working vacations to describe queueing phenomena that arise in an advanced computing environment of virtualized servers operated by the infrastructure owners. In the proposed queue the inter-arrival times of jobs requesting servers follow a Generalized Exponential distribution. To model a maintenance activity, we assume that a certain number of servers simultaneously goes to a maintenance state for a random period when they complete the service of requests and find no further jobs in the waiting line. We derive an expression for the steady-state probabilities and prove a conditional stochastic decomposition property. By a relatively simple model we are able to prove a property which has a significant impact on the organization of maintenance activities of virtualized servers. It means that instead of migrating virtual servers to expensive physical backup servers during software maintenance, a wise and simple strategy based on the vacation approach can be used. Moreover, it is theoretically proved that the system is not overloaded if we organize the maintenance according to the vacation model. We believe that our model can be useful for administrators to choose an appropriate parameter set for the maintenance activities.

A new solution for a queueing model of a manufacturing cell with negative customers under a rotation rule

In this paper, we consider a queueing model extension for a manufacturing cell composed of a machining center and several parallel downstream production stations under a rotation rule. A queueing model is extended with the arrival processes of negative customers to capture failures of production stations, reorganization of works and disasters in the manufacturing cell. We present an exact solution for the steady-state probabilities of the proposed queueing model. The solution does not require the approximation of the infinite sum. In addition, it provides an alternative way to compute the rate matrix for the matrix-geometric method as well.