Yaakov Kogan

VoIP reliability: a service provider's perspective

Voice over IP services offer important revenue-generating opportunities, as well as many technical challenges in providing high-quality services. Users have come to expect highly available telecommunications services with high-quality voice. Service providers need reliable high-performance networks to meet user expectations, and must be able to guarantee performance and reliability to their customers. In converged voice and data networks, the network infrastructure must deliver very high quality and availability for some customer needs, while also providing low-cost high-capacity bandwidth for other needs. The use of quality of service mechanisms to provide prioritization for various traffic types is a key element needed for voice and data network convergence. However, it is not sufficient if the underlying networks are unreliable. The focus of this article is to address the reliability aspects of VoIP services, including the underlying IP networks.

Asymptotic evaluation of closed queueing networks with many stations

Asymptotic formulas are derived for the partition function of multichain closed product form networks with groups of stations, each group consisting of many identical stations. The derivation of the asymptotic expansion is based on an integral representation of the partition function in a multidimensional complex space and its evaluation using the saddle point method. The saddle point method is also used to derive an iterative algorithm which reduces the problem of solving the multichain network to a set of single chain problems. The accuracy of the approximations is evaluated in two case studies: a memory interference model in a multiprocessing system and a model of a multiprogramming system.

Bottleneck analysis in multiclass closed queueing networks and its application

Asymptotic behavior of queues is studied for large closed multi-class queueing networks consisting of one infinite server station with K classes and M processor sharing (PS) stations. A simple numerical procedure is derived that allows us to identify all bottleneck PS stations. The bottleneck station is defined asymptotically as the station where the number of customers grows proportionally to the total number of customers in the network, as the latter increases simultaneously with service rates at PS stations. For the case when K=M=2, the set of network parameters is identified that corresponds to each of the three possible types of behavior in heavy traffic: both PS stations are bottlenecks, only one PS station is a bottleneck, and a group of two PS stations is a bottleneck while neither PS station forms a bottleneck by itself. In the last case both PS stations are equally loaded by each customer class and their individual queue lengths, normalized by the large parameter, converge to uniformly distributed random variables. These results are directly generalized for arbitrary K=M. Generalizations for K≠M are also indicated. The case of two bottlenecks is illustrated by its application to the problem of dimensioning bandwidth for different data sources in packet-switched communication networks. An engineering rule is provided for determining the link rates such that a service objective on a per-class throughput is satisfied.

Call routing to distributed queues: Is FIFO really better than MED?

New services providing automatic call distribution in the network have been one of the most hotly contested areas in the USA telecommunications arena in recent years. This has been fueled by increasing demand from large corporations for intelligent network routing that will keep their geographically distributed telemarketing/service centers operating with maximum efficiency. This paper compares two basic strategies for a network call distributor: a centralized FIFO queue and a distributed queueing strategy called Minimum‐Expected‐Delay (MED). According to MED, a central controller routes each arrival to the node that minimizes its expected delay (waiting time). Our main result qualifies the conventional wisdom that perceives FIFO as optimal. We show that the waiting time under FIFO is not stochastically smaller than that under MED. Furthermore, we prove that the waiting time distribution functions intersect at a single point. Numerical experiments suggest that, for certain performance criteria and over a range of parameters of interest, MED can actually outperform FIFO.

Asymptotic analysis for closed multichain queueing networks with bottlenecks

We consider a two-chain exponential queueing network with a large number of customers that consists of one infinite-server (IS) station and two processor-sharing (PS) or FCFS single-server stations. The asymptotic behavior of the partition function is studied for such a network when one or both PS (FCFS) nodes are heavily loaded. The results are derived using methods of multidimensional complex analysis (the theory of homologies and residues) and the saddle-point method.

Reliability Metrics for Routers in IP Networks

The reliability of modern provider edge routers, which have a large variety of interface cards, cannot be accurately characterized by a single downtime or reliability metric because it requires averaging the contributions of the various line cards that may hide the poor reliability of some components. This challenge is addressed by introducing granular metrics for quantifying the reliability of IP routers. Section 3.2 provides an overview of the main router elements and redundancy mechanisms. In Section 3.3, a simplified router reliability model is used to demonstrate the application of different reliability metrics. In Section 3.4, metrics are defined for measuring the reliability of IP routers in production networks. Section 3.5 provides an overview of challenges with measuring end-to-end availability.

Distribution of processor-sharing customers for a large closed system with multiple classes

A closed processor-sharing (PS) system with multiple customer classes is considered. The system consists of one infinite server (IS) station and one PS station. For a system with a large number of customers, a saturated PS station, and an arbitrary number of customer classes, asymptotic approximations to the stationary distribution of the total number of customers at the PS station are derived. The asymptotics for the probability mass function is described by a quasi-potential function, which defines the exponential decay for the distribution, and a state-dependent preexponential factor. Both functions have an explicit expression in terms of the solution at each point x of a polynomial equation whose order equals the number of classes and whose coefficients are explicit functions of x. The quasi-potential function at its minimum point provides the logarithmic asymptotics for the normalization constant, and the asymptotic approximation for the variance is inversely proportional to the second derivative of ...

Exact and asymptotic solutions for models of new telecommunication services

A new product-form, finite capacity network model is described for the blocking analysis of modern telecommunication services such as automatic redial, video on demand, interactive TV and video telephony. It allows multiple finite sources requiring random routes and a random number of resource units from one or several resource types. We obtain a simple closed-form expression for the generating partition function and from that derive three computational methods based on numerical inversions, asymptotic approximations and recursion relations. The main concepts from the asymptotic method are also used in the numerical inversion method to justify speed-up of this method for large models. Numerical examples are presented to illustrate the effectiveness of the procedures.

Error bounds for asymptotic approximations of the partition function

We consider Markovian queueing models with a finite number of states and a product form solution for its steady state probability distribution. Starting from the integral representation for the partition function in complex space we construct error bounds for its asymptotic expansion obtained by the saddle point method. The derivation of error bounds is based on an idea by Olver applicable to integral transforms with an exponentially decaying kernel. The bounds are expressed in terms of the supremum of a certain function and are asymptotic to the absolute value of the first neglected term in the expansion as the large parameter approaches infinity. The application of these error bounds is illustrated for two classes of queueing models: loss systems and single chain closed queueing networks.

Evaluation of impact of backbone outages in IP networks

Nationwide IP networks typically include nodes in major cities and the following elements: customer equipment, access routers, backbone routers, peering routers, access links connecting customer equipment to access routers, access routers to backbone routers, and backbone links interconnecting backbone routers. The part of this network consisting of backbone routers and related interconnecting links is referred to as the “backbone”. We develop a new approach for accurately computing the Availability measure of IP networks by directly simulating each type of backbone outage event and its impact on traffic loss. We use this approach to quantify availability improvement as a result of introducing various technological changes in the network such as IGP tuning, high availability router architecture, MPLS-TE and Fast Reroute. A situation, where operational backbone links do not have enough spare capacity to carry additional traffic during the outage time, is referred to as bandwidth loss. We concentrate on one unidirectional backbone link and derive asymptotic approximations for the expected bandwidth loss in the framework of generalized Erlang and Engset models when the total number of resource units and request arrival rates are proportionally large. Simulation results demonstrate good accuracy of the approximations.