Rostislav Razumchik

Simulation Of Overload Control In SIP Server Networks.

In this study, we investigated a signalling load control mechanism for SIP server networks and developed a corresponding queuing model. The so-called hop-by-hop overload control, known from recent IETF drafts and RFCs, was considered and a similar buffer overload control scheme which was developed for the SS7 signalling link in ITU-T Recommendation Q.704, was proposed. The mechanism is based on hysteretic load control with thresholds for reducing potential oscillations between the control-on and control-off states under certain loading conditions. Adjustment of three types of thresholds – the overload onset threshold, the overload abatement threshold, and the overload discard threshold – makes possible the regulation of signalling traffic to meet blocking requirements. In this study, we built and analyzed the M |M |1 queue with bi-level hysteretic input load control. A numerical example illustrating the control mechanism that minimizes the return time from overloading states satisfying the throttling and mean control cycle time constraints is also presented.

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

Abstract 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 given

On analytical model for optimal SIP server hop-by-hop overload control

In this paper, we present analytical results of the analysis of the queueing system that models signalling hop-by-hop load control mechanism for SIP server. The so-called hop-by-hop overload control, known from recent IETF drafts and RFCs, is based on hysteretic load control with two thresholds for reducing potential oscillations between the control-on and control-off states under certain loading conditions. Adjustment of thresholds values makes possible the load control of signalling traffic and therefore meeting blocking requirements. New approach that allows fast computation of joint stationary probability distribution of finite M2|M|1|R queue with bi-level hysteretic input load control is proposed. Illustrative numerical example is given to demonstrate some optimization issues.

Ergodicity And Perturbation Bounds For Inhomogeneous Birth And Death Processes With Additional Transitions From And To The Origin

Abstract Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, time-dependent analysis is more meaningful. In this paper, transient analysis of one class of Markov processes defined on non-negative integers, specifically, inhomogeneous birth and death processes allowing special transitions from and to the origin, is carried out. Whenever the process is at the origin, transition can occur to any state, not necessarily a neighbouring one. Being in any other state, besides ordinary transitions to neighbouring states, a transition to the origin can occur. All possible transition intensities are assumed to be non-random functions of time and may depend (except for transition to the origin) on the process state. To the best of our knowledge, first ergodicity and perturbation bounds for this class of processes are obtained. Extensive numerical results are also provided.

Analytical Modelling And Simulation For Performance Evaluation Of SIP Server With Hysteretic Overload Control.

Major standards organizations, ITU, ETSI, and 3GPP have all adopted SIP as a basic signalling protocol for NGN. The current SIP overload control mechanism is unable to prevent congestion collapse and may spread the overload condition throughout the network. In this paper, we investigate one of the implementations of loss based overload control scheme developed by IETF work group which uses hysteretic load control technique on the server side for preventing its overloading. Two different approaches to calculate performance measure of SIP server are introduced. We follow an analytical modelling approach to construct and analyse SIP server model in the form of queuing system with finite buffer occupancy and two-level hysteretic overload control. The formulas for stationary probabilities and the mean return time in the set of normal states were obtained. Simulation is the other approach which allows to eliminate disadvantages of analytical modelling. At present, there is no simulator for modelling of SIP servers in overload conditions with an application of overload control mechanisms which are currently under development by IETF. Approaches to its programming implementations which reflects the protocols and functions that are fully or partially built into the original SIP systems are proposed in the paper.

Analysis of Queueing System with Constant Service Time for SIP Server Hop-by-Hop Overload Control

Consideration is given to the analysis of queueing system M 2|D|1|R with bi-level hysteretic input load control that can model signalling hop-by-hop overload control mechanism for SIP servers described in RFC 6357. Bi-level hysteretic input load control implies that system may be in three states (normal, overloaded, blocking), depending on the total number of customers present in it, and upon each state change input flow rate is adjusted. New approach that allows fast computation of joint stationary probability distribution is proposed, expressions for important performance characteristics are given.

Queuing Model for SIP Server Hysteretic Overload Control with Bursty Traffic

In this paper, we develop a mathematical model of a load control mechanism for SIP server signaling networks based on a hysteretic technique. We investigate loss-based overload control, as proposed in recent IETF documents. The queuing model takes into account three types of system state – normal load, overload, and discard. The hysteretic control is made possible by introducing two thresholds, L and H, in the buffer of total size R. We denote the mathematical model using the modified Kendall notation as an \(MMPP|M|1|\left\langle L,H\right\rangle |R\) queue with hysteretic load control and bursty input flow. Algorithms for computation the key performance parameters of the system were obtained. A numerical example illustrating the control mechanism that minimizes the return time from overloading states satisfying the throttling and mean control cycle time constraints is also presented.

On Mean Return Time in Queueing System with Constant Service Time and Bi-level Hysteric Policy

Single server queueing system with two Poisson input flows of rate λ 1 and λ 2, finite queue of size R − 1 < ∞ and bi-level hysteretic policy is considered. Customers of λ 1 flow are served with relative priority. Customers of both flows are served with the same constant service time. Bi-level hysteretic policy implies that system may be in three states (normal, overload, blocking), depending on the total number of customers present in it. New method for calculation of mean return time to normal operation state is proposed.

Delay analysis of a queue with re-sequencing buffer and Markov environment

There are simple service disciplines where the system time of a tagged customer depends only on the customers arriving in the system earlier (for example first-in-first-out (FIFO)) or later (for example LIFO) than the tagged one. In this paper we consider a single-server queueing system with two infinite queues in which the system time of a tagged customer may depend on both the customers arriving in the system earlier and later than the tagged one. New regular customers arrive in the system according to Markov arrival process (MAP) flow, occupy one place in the buffer and receive service in FIFO order. External re-sequencing signals also arrive at the system according to (different) MAP flow. Each re-sequencing signal transforms one regular customer into a delayed one by moving it to another queue (re-sequencing buffer), wherefrom it is served with lower priority than the regular ones. Service times of customers from both queues also have MAP distribution different from those which govern arrivals. Queueing system with memoryless ingredients (arrival, service, resequencing) has already been a subject of extensive research. In this paper we investigate how the essential analytical properties of scalar functions, which made the analysis of the memoryless system feasible, can be extended to the case of a Markov environment.

On temporal characteristics in an exponential queueing system with negative claims and a bunker for ousted claims

We consider a queueing system with Poisson input streams of positive and negative claims, an infinite collector, and exponential service. A negative claim ousts a positive claim out of the collector queue and moves it to a bunker of unbounded capacity. If the collector is empty then a negative claim leaves the system with no influence on it. After a claim is serviced, the device receives the next claim from the collector or, if the collector is empty, from the bunker. For different combinations of FIFO and LIFO orders of choosing a claim for service from the collector’s queue, choosing a claim for service from the bunker’s queue, and ousting claims from the collector to the bunker, we obtain formulas for computing the stationary waiting time distribution for a claim to begin service and other temporal characteristics.