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

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

Joint stationary distribution of m queues in the N -server queueing system with reordering [СОВМЕСТНОЕ СТАЦИОНАРНОЕ РАСПРЕДЕЛЕНИЕ ЧИСЛА ЗАЯВОК В m ОЧЕРЕДЯХ В N -КАНАЛЬНОЙ СИСТЕМЕ ОБСЛУЖИВАНИЯ С ПЕРЕУПОРЯДОЧЕНИЕМ ЗАЯВОК]

The paper considers a continuous-time N -server queueing system with a buffer of infinite capacity and customer reordering. The Poisson flow of customers arrives at the system. Service times of customers at each server are exponentially distributed with the same parameter. Each customer obtains a sequential number upon arrival. The order of customers upon arrival should be preserved upon departure from the system. Customers which violated the order form different queues in the reordering buffer which has infinite capacity. If there are n, n = 1, N, customers in servers, then the latest customer to occupy a server is called the 1st level customer, the last but one - the 2nd level customer,..., the first - the nth level customer. Customers in the reordering buffer that arrived between the 1st level and the 2nd level customers, form the queue number one. Customers, which arrived between the 2nd level and the 3rd level customers, form the queue number two, etc. Customers, which arrived between the N th level and the (N − 1)th level customers, form the queue number (N − 1) in the reordering buffer. Mathematical relations in terms of Z-transform, which make it possible to calculate the joint stationary distribution of the number of customers in the buffer, servers, and in the 1st, 2nd,..., mth queues (m = 1, N − 1) in the reordering buffer, are obtained. © 2015 Federal Research Center "Computer Science and Control" of Russian Academy of Sciences. All rights reserved

Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies

Hysteretic control of arrivals is one of the most easy-to-implement and effective solutions of overload problems occurring in SIP-servers. A mathematical model of an SIP server based on the queueing system M[X]|G|1(L,H)|(H,R) with batch arrivals and two hysteretic loops is being analyzed. This paper proposes two analytical methods for studying performance characteristics related to the number of customers in the system. Two control policies defined by instants when it is decided to change the system’s mode are considered. The expression for an important performance characteristic of each policy (the mean time between changes in the system mode) is presented. Numerical examples that allow comparison of the efficiency of both policies are give