Iterative Algorithm for Threshold Calculation in the Problem of Routing Fixed Size Jobs to Two Parallel Servers, Journal of Telecommunications and Information Technology, 2015, nr 3

At present, solutions of many practical problems require significant computational resources and systems (grids, clouds, clusters etc.), which provide appropriate means are constantly evolving. The capability of the systems to fulfil quality of service requirements pose new challenges for the developers. One of the well-known approaches to increase system performance is the use of optimal scheduling (dispatching) policies. In this paper the special case of the general problem of finding optimal allocation policy in the heterogeneous n-server system processing fixed size jobs is considered. There are two servers working independently at constant but different speeds. Each of them has a dedicated queue (of infinite capacity) in front of it. Jobs of equal size arrive at the system. Inter-arrival times are i.i.d. random variables with general distribution with finite mean. Each job upon arrival must be immediately dispatched to one of the two queues wherefrom it will be served in FCFS manner (no pre-emption). The objective is the minimization of mean job sojourn time in the system. It is known that under this objective the optimal policy is of threshold type. The authors propose scalable fast iterative non-simulation algorithm for approximate calculation of the policy parameter (threshold). Numerical results are given

Estimation of Network Disordering Eff ects by In-depth Analysis of the Resequencing Bu ffer Contents in Steady-state, Journal of Telecommunications and Information Technology, 2016, nr 1

The paper is devoted to the analytic analysis of resequencing issue, which is common in packet networks, using queueing-theoretic approach. The authors propose the mathematical model, which describes the simplest setting of packet resequencing, but which allows one to make the first step in the in-depth-analysis of the queues dynamics in the resequencing buffer. Specifically consideration is given to N-server queueing system (N > 3) with single infinite capacity buffer and resequencing, which may serve as a model of packet reordering in packet networks. Customers arrive at the system according to Poisson flow, occupy one place in the buffer and receive service from one of the servers, which is exponentially distributed with the same parameter. The order of customers upon arrival has to be preserved upon departure. Customers, which violated the order are kept in resequencing buffer which also has infinite capacity. It is shown that the resequencing buffer can be considered as consisting of n, 1 ≤ n ≤ N −1, interconnected queues, depending on the number of busy servers, with i-th queue containing customers, which have to wait for i service completions before they can leave the system. Recursive algorithm for computation of the joint stationary distribution of the number of customers in the buffer and servers, and each queue in resequencing buffer are being obtained. Numerical examples, which show the dynamics of the characteristics of the queues in resequencing buffer are given

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

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

Hysteretic Control Technique for Overload Problem Solution in Network of SIP Servers

This paper contains research and development results concerning application of hysteretic control principles to solve SIP servers overload problem, which is known from a number of IETF standards and scientific papers published over the past few years. The problem is that SIP protocol, being the application layer protocol, by default has no build-in means of overload control, as, for example, SS7, MTP2 and MTP3 protocols. It was the SS7 network, where a threshold mechanism of hysteretic signalling load control was first implemented. In this paper we describe the main up-to-date solutions of an overload control problem in a signalling network, and develop analytical models of hysteretic control, which are useful in the development of load management functions of SIP servers. We also propose the design of Open SIP signalling Node (OSN) software architecture which is intended to be used for simulations and comparison of various overload control mechanisms

On the Three Methods for Bounding the Rate of Convergence for some Continuous-time Markov Chains

Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is particularly suited to describe evolutions of the total number of customers in (in)homogeneous $M/M/S$ queueing systems with possibly state-dependent arrival and service intensities, batch arrivals and services. One of the methods is based on the logarithmic norm of a linear operator function; the other two rely on Lyapunov functions and differential inequalities, respectively. Less restrictive conditions (compared to those known from the literature) under which the methods are applicable, are being formulated. Two numerical examples are given. It is also shown that for homogeneous birth-death Markov processes defined on a finite state space with all transition rates being positive, all methods yield the same sharp upper bound

Algebraic method for approximating joint stationary distribution in finite capacity queue with negative customers and two queues [АЛГЕБРАИЧЕСКИЙ МЕТОД ПРИБЛИЖЕННОГО РАСЧЕТА СТАЦИОНАРНОГО РАСПРЕДЕЛЕНИЯ В СИСТЕМЕ ОБСЛУЖИВАНИЯ КОНЕЧНОЙ ЕМКОСТИ С ОТРИЦАТЕЛЬНЫМИ ЗАЯВКАМИ И ДВУМЯ ОЧЕРЕДЯМИ]

Consideration is given to the single-server queueing system (QS) with a Poisson flow of (ordinary) customers and Poisson flow of negative customers. There is a queue of capacity k (0 < k < ∞), where ordinary customers wait for service. If an ordinary customer finds the queue full upon an arrival, it is considered to be lost. Each negative customer upon arrival moves one ordinary customer from the queue, if it not empty, to another queue (bunker) of capacity r (0 < r < ∞) and after that it leaves the system. If upon arrival of a negative customer the queue is not empty and the bunker is full, the negative customer and one ordinary customer from the queue leave the system. In all other cases, an arrival of a negative customer has no effect on the system. Customers from bunker are served with relative priority (i. e., a customer from bunker enters server if only there are no customers in the queue to be served). Service times of customers from both the queue and the bunker are exponentially distributed with the same parameter. Purely algebraic method based on generating functions, Chebyshev and Gegenbauer polynomials for approximate calculation of joint stationary probability distribution is presented for the case k = r. Numerical examples, showing both pros and cons of the method are provided. © 2015 Federal Research Center "Computer Science and Control" of Russian Academy of Sciences. All rights reserved