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

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

Система MAP∕G∕1∕∞ с инверсионным порядком обслуживания и вероятностным приоритетом, функционирующая в дискретном времени

This paper considers a discrete-time queueing system MAP∕G∕1∕∞ that is determined as follows. Upon arrival into the system of a new customer its length is compared with the (remaining) length of the customer in the device and with some probability which depends only on this two lengths, a new arrival will occupy the server while pushing out a servicing customer to the first place in the queue, and with the supplemental probability, alternatively, the newly arrived one occupies the first position in the queue (inversive service order and probabilistic priority). The main stationary characteristics of such systems behavior have been found. A number of numerical examples are presented according to found analytical formulae.Рассматривается функционирующая в дискретном времени система массового обслуживания MAP∕G∕1∕∞ с дисциплиной обслуживания, при которой поступающая в систему заявка с некоторой вероятностью, зависящей только от её длины и (остаточной) длины заявки на приборе, становится на прибор, вытесняя обслуживавшуюся ранее на первое место в очередь, или с дополнительной вероятностью сама занимает первое место в очереди (инверсионный порядок обслуживания с вероятностным приоритетом). Для этой системы найдены основные стационарные характеристики функционирования. Приведены примеры расчётов, проведённых с помощью полученных аналитических соотношений

SRPT Scheduling for Web Servers

This note briey summarizes some results from two papers: [4] and [23]. These papers pose the following question: Is it possible to reduce the expected response time of every request at a web server, simply by changing the order in which we schedule the requests? In [4] we approach this question analytically via an M/G/1 queue. In [23] we approach the same question via implementation involving an Apache web server running on Linux

A queueing system with negative claims and a bunker for superseded claims in discrete time

We consider a discrete time single-line queueing system with independent geometric streams of regular and negative claims, infinite buffer, and geometric service. A negative claim pushes a regular claim out of the buffer queue and moves it to a bunker of infinite capacity. If the buffer is empty, a negative claim leaves the system without any effect. After servicing a claim, the system receives the next claim from the buffer, if it is not empty, or from the bunker. We obtain relations that allow computing stationary distributions for queues in the buffer and the bunker. © 2009 Pleiades Publishing, Ltd

First passage times in M2 [X] | G | 1 | R queue with hysteretic overload control policy

One of the reported approaches towards the solution of overload problem in networks of SIP servers is the implementation of multi-level hysteretic control of arrivals in SIP servers. Each level, being the parameter of the policy, specifies operation mode of SIP server i.e. it implicitly indicates what SIP server must do with the arriving packets. The choice of parameters' values is not guided by standards and is usually left for the network owner. In general, all operation modes of the considered policy can be grouped into two groups: normal mode (when all arriving packets are accepted) and congested mode (when part or all arriving packets are being dropped). Such grouping may serve as the criteria for choosing parameters' values of the policy: pick those values which minimize SIP server sojourn time in congested mode. In this short note we propose some analytical results which facilitate the solution of stated minimization problem. The considered mathematical model of SIP server is the queueing system M2[X]|G|1|R with batch arrivals and bi-level hysteretic control policy, which specifies three operation modes: normal (customers both flows are accepted), overload (only customers from one flow are accepted), discard (customers from both flows are blocked/lost)). The switching between modes can occur only on service completions. Analytical method allowing computation of stationary sojourn times in different operation modes (as well as first passage times between modes) is presented in brief. Numerical example is given. © 2016 Author(s)

On decomposition of closed networks with dependent service times

The problem of decomposition of closed data communication networks admitting the dependence of times taken to transfer messages over different channels is considered

Stationary time characteristics of the GI/M/n/∞ system with some variants of the generalized renovation discipline

Consideration was given to the queuing system with recurrent arrivals, exponential distribution of the service time, infinite buffers, and the following variants of the discipline of generalized renovation and service: inversive order of renovation with direct order of customer service and direct and inversive orders of renovation with inversive order of customer service. For the serviced and lost customers, the stationary time characteristics of sojourn in the buffer were determined © 2009 Pleiades Publishing, Ltd