Multi-threshold Control of the BMAP/SM/1/K Queue with Group Services

We consider a finite capacity queue in which arrivals occur according to a batch Markovian arrival process (BMAP). The customers are served in groups of varying sizes. The services are governed by a controlled semi-Markovian process according to a multithreshold strategy. We perform the steady-state analysis of this model by computing (a) the queue length distributions at departure and arbitrary epochs, (b) the Laplace-Stieltjes transform of the sojourn time distribution of an admitted customer, and (c) some selected system performance measures. An optimization problem of interest is presented and some numerical examples are illustrated

Queueing System with Potential for Recruiting Secondary Servers

In this paper, we consider a single server queueing system in which the arrivals occur according to a Markovian arrival process (MAP). The served customers may be recruited (or opted from those customers’ point of view) to act as secondary servers to provide services to the waiting customers. Such customers who are recruited to be servers are referred to as secondary servers. The service times of the main as well as that of the secondary servers are assumed to be exponentially distributed possibly with different parameters. Assuming that at most there can only be one secondary server at any given time and that the secondary server will leave after serving its assigned group of customers, the model is studied as a QBD-type queue. However, one can also study this model as a G I/M/1-type queue. The model is analyzed in steady state, and a few illustrative numerical examples are presented

Statistical Analysis and Modeling of SIP Traffic for Parameter Estimation of Server Hysteretic Overload Control, Journal of Telecommunications and Information Technology, 2013, nr 4

The problem of overload control in Session Initiation Protocol (SIP) signaling networks gives rise to many questions which attract researchers from theoretical and practical point of view. Any mechanism that is claimed to settle this problem down demands estimation of local (control) parameters on which its performance is greatly dependent. In hysteretic mechanism these parameters are those which define hysteretic loops. In order to find appropriate values for parameters one needs adequate model of SIP traffic flow circulating in the network under consideration. In this paper the attempt is made to address this issue. Analysis of SIP traffic collected from telecommunication operator’s network is presented. Traffic profile is built. It is shown that fitting with Markov Modulated Poisson Process with more than 2 phases is accurate. Estimated values of its parameters are given

Analysis of an MAP/PH/1 Queue with Flexible Group Service

Abstract A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer's service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace–Stieltjes transform of the waiting time is obtained. Results are numerically illustrated

Threshold Queueing to Describe the Fundamental Diagram of Uninterrupted Traffic

Queueing because of congestion is an important aspect of road traffic. This paper provides a novel threshold queue that models the empirical shape of the fundamental diagram. In particular, we show that our threshold queue with two service phases captures the capacity drop that is eminent in the fundamental diagram of modern traffic. We use measurements on a Danish highway to illustrate that our threshold queue is indeed capable of capturing the fundamental diagram of real-world traffic systems. We furthermore indicate the modelling power of our threshold queue via a sensitivity study showing that our model is able to capture a wide range of shapes for the fundamental diagram

Mathematical Analysis of Queue with Phase Service: An Overview

We discuss various aspects of phase service queueing models. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent

Statistical Analysis of Message Delay in SIP Proxy Server, Journal of Telecommunications and Information Technology, 2014, nr 4

Single hop delay of SIP message going through SIP proxy server operating in carriers backbone network is being analyzed. Results indicate that message sojourn times inside SIP server in most cases do not exceed order of tens of milliseconds (99% of all SIP-I messages experience less than 21 ms of sojourn delay) but there were observed very large delays which can hardly be attributed to message specic processing procedures. It is observed that delays are very variable. Delay components distribution that is to identied are not exponentially distributed or nearly constant even per message type or size. The authors show that measured waiting time and minimum transit time through SIP server can be approximated by acyclic phase-type distributions but accuracy of approximation at very high values of quantiles depends on the number outliers in the data. This nding suggests that modeling of SIP server with queueing system of GjPHjc type may server as an adequate solution

Analysis of some batch arrival queueing systems with balking, reneging, random breakdowns, fluctuating modes of service and Bernoulli schedulled server vacations.

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe purpose of this research is to investigate and analyse some batch arrival queueing systems with Bernoulli scheduled vacation process and single server providing service. The study aims to explore and extend the work done on vacation and unreliable queues with a combination of assumptions like balking and re-service, reneging during vacations, time homogeneous random breakdowns and fluctuating modes of service. We study the steady state properties, and also transient behaviour of such queueing systems. Due to vacations the arriving units already in the system may abandon the system without receiving any service (reneging). Customers may decide not to join the queue when the server is in either working or vacation state (balking). We study this phenomenon in the framework of two models; a single server with two types of parallel services and two stages of service. The model is further extended with re-service offered instantaneously. Units which join the queue but leave without service upon the absence of the server; especially due to vacation is quite a natural phenomenon. We study this reneging behaviour in a queueing process with a single server in the context of Markovian and non-Markovian service time distribution. Arrivals are in batches while each customer can take the decision to renege independently. The non-Markovian model is further extended considering service time to follow a Gamma distribution and arrivals are due to Geometric distribution. The closed-form solutions are derived in all the cases. Among other causes of service interruptions, one prime cause is breakdowns. We consider breakdowns to occur both in idle and working state of the server. In this queueing system the transient and steady state analysis are both investigated. Applying the supplementary variable technique, we obtain the probability generating function of queue size at random epoch for the different states of the system and also derive some performance measures like probability of server‟s idle time, utilization factor, mean queue length and mean waiting time. The effect of the parameters on some of the main performance measures is illustrated by numerical examples to validate the analytical results obtained in the study. The Mathematica 10 software has been used to provide the numerical results and presentation of the effects of some performance measures through plots and graphs

Journal of Telecommunications and Information Technology, nr 4

kwartalni