Alexander V. Pechinkin

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.

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.

A discrete-time queueing system with optional LCFS discipline

We consider a discrete-time queueing system in which the arriving customers decide with a certain probability to be served under a LCFS-PR discipline and with complementary probability to join the queue. The arrivals are assumed to be geometrical and the service times are arbitrarily distributed. The service times of the expelled customers are independent of their previous ones.We carry out an extensive analysis of the system developing recursive formulae and generating functions for the steady-state distribution of the number of customers in the system and obtaining also recursive formulae and generating functions for the stationary distribution of the busy period and sojourn time as well as some performance measures.

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.

A Discrete-Time Queueing System With Different Types Of Displacement.

The performance prediction in communication, jobs processing in computers, etc, are always influenced by the customers behavior and the provision of this additional information will be useful in upgrading the service. Our paper is concerned under a loss and trigger protocol where each customer has a service requirement which may depend on the arrival of a positive or negative customer. In our study we consider customer expulsions and different types of customers displacements taking into account or not its past time of service. The main purpose of this work is to spread the discrete-time queueing theory about expulsions and displacement. We provide a unified way to handle the combinations of different conditions such as positive arrival, negative arrival, trigger movements, past time in service, etc. INTRODUCTION An investigation of discrete-time queueing system is important due to their application to slotted systems such as communication systems and other related areas and therefore it has been found more appropriate than their continuous-time counterpart. The study of discrete-time queues was initiated by (Meisling 1958; Birdsall et al. 1962; Powell et al. 1967). Reference works and more detailed applications on discrete-time queueing theory include the monographs (Bruneel and Kim 1993; Takagi 1993). Further, a detailed treatment regarding this subject can be found in a two-volume book on applied probability (Hunter 1983). A rapid increase in the literature on queueing system with negative arrivals are analyzed extensively in continuous-time models but not so much in discrete-time. The arrival of a negative customer to a queueing system causes one ordinary customer to be removed or killed if any is present. The pioneer work on discrete-time considering negative arrivals without retrials can be found in (Atencia and Moreno 2004; Atencia and Moreno 2005) where the authors considered several killing strategies for the negative customers. For a survey on this topics the authors refer to (Gelenbe and Label 1998) and (Artalejo 2000), for applications on engineering to (Chao et al. 1999) and for application in communication networks we refer to (Harrison et al. 2000) and (Park et al. 2009). In many real problems it is also interesting to consider the movement of jobs, customers, etc., from one place to another. This mechanism is called a synchronized or triggered motion, see for example (Artalejo 2000) and (Gelenbe and Label 1998) and concerning with inverse order discipline we refer to (Pechinkin and Svischeva 2004), (Pechinkin and Shorgin 2008) and (Cascone et al. 2011). For service interruptions with expulsions we refer to (Atencia and Pechinkin 2012) and (Atencia et al. 2013). THE MATHEMATICAL MODEL We consider a discrete-time queueing system where the time axis is segmented into a sequence of equal time intervals (called slots). It is assumed that all queueing activities (arrivals, departures and retrials) occur at the slot boundaries, and therefore, they may take place at the same time. That is why we must detail the order in which the arrivals and departures occur in case of simultaneity in a discrete-time system. Basically, there are two rules: (i) If an arrival takes precedence over a departure, it is identified with Late Arrival System (LAS) (see Figure 1(a)); (ii) if a departure takes precedence over an arrival, it is recognized by Early Arrival System (EAS) (see Figure 1(b)). The former case is also known as Arrival First (AF) policy and the latter as Departure First (DF) policy. For more details on these and related concepts, see (Gravey and Hebuterne 1992) and (Hunter 1983). Let us note, that for mathematical convenience, we will follow the second policy, that is the departures occur at the moment immediately before the slot boundaries, Proceedings 27th European Conference on Modelling and Simulation ©ECMS Webjorn Rekdalsbakken, Robin T. Bye, Houxiang Zhang (Editors) ISBN: 978-0-9564944-6-7 / ISBN: 978-0-9564944-7-4 (CD) but arrivals occurs at the moment immediately after the slot boundaries.

Threshold-based queuing system for performance analysis of cloud computing system with dynamic scaling

Cloud computing is promising technology to manage and improve utilization of computing center resources to deliver various computing and IT services. For the purpose of energy saving there is no need to unnecessarily operate many servers under light loads, and they are switched off. On the other hand, some servers should be switched on in heavy load cases to prevent very long delays. Thus, waiting times and system operating cost can be maintained on acceptable level by dynamically adding or removing servers. One more fact that should be taken into account is significant server setup costs and activation times. For better energy efficiency, cloud computing system should not react on instantaneous increase or instantaneous decrease of load. That is the main motivation for using queuing systems with hysteresis for cloud computing system modelling. In the paper, we provide a model of cloud computing system in terms of multiple server threshold-based infinite capacity queuing system with hysteresis and noninstantanuous server activation. For proposed model, we develop a method for computing steady-state probabilities that allow to estimate a number of performance measures.

A two-priority queueing system with trunk reservation, infinite capacity buffers for customers of both priorities, and different service intensities for high-priority and non-priority customers

A two-priority queueing system with trunk reservation, Poisson input flows of both priorities customers, infinite buffers and different exponential distributions of both priorities customers service times is considered. Trunk reservation means that there are some channels which can be used only by customers of high priority. Analytic relations to calculate the main stationary distributions of both priorities customers quantities are obtained.