Multirate Loss Research Articles

Performance metrics of a multirate resource sharing teletraffic model with finite sources under the threshold and bandwidth reservation policies

The authors propose a new multirate teletraffic loss model of a single link with certain capacity that accommodates different service-classes whose calls come from finite traffic sources. Calls compete for the available link bandwidth under the combination of the threshold (TH) and the bandwidth reservation (BR) policies. The TH policy can provide different quality of service among service-classes by limiting calls of each service-class up to a certain number, which is a predefined TH, which can be different for each service-class. The BR policy reserves part of the available link bandwidth to benefit calls of high bandwidth requirements. They show that the proposed model, without the BR policy, has a product form solution (PFS) and prove recursive formulas for the efficient calculation of the call-level performance metrics, such as time and call congestion probabilities as well as link utilisation. The combination of the TH and BR policies destroys the PFS of the model. However, they show that approximate but recursive formulas still exist for the efficient calculation of the call-level performance metrics. The accuracy of the proposed formulas is verified through simulation and found to be very satisfactory.

Congestion in large balanced multirate networks

In this paper, we obtain analytical approximations for various performance measures for a large fluid stochastic network that operates under a balanced fair bandwidth allocation policy. Balanced fairness results in the insensitivity of the stationary distribution of the number in the system to the precise distribution of file sizes. Balanced fairness has been shown to coincide with proportional fairness in large systems. The model we consider is that of servers operating under balanced fair rate allocations that are accessed by a large number of independent heterogeneous flows characterized by their arrival rate and general distributions of the file sizes; and a maximum service rate associated with each type of flow. The largeness of the system is parameterized by a scaling parameter that scales the arrival rates and capacity in such a way that the ratio is fixed. By exploiting a connection of the congestion probabilities with multirate Erlang loss systems, we use local limit large deviation methods to obtain accurate approximations as the scaling increases. The paper first discusses the single link case which is then extended to the case of a parking lot model that is a special case of tree networks.

Engset multi-rate state-dependent loss models

Call blocking probabilities (CBP) are a key index of quality of service assessment in multi-rate networks. We focus on the CBP calculation in single link loss models where calls of each service-cla...

Call blocking probabilities in a traffic-groomed tandem optical network

In this paper, we consider an optical network consisting of N nodes arranged in tandem. We assume traffic grooming, which permits multiple sub-rate traffic streams to be carried on the same wavelength. This optical network is modeled by a tandem queueing network of multi-rate Erlang loss nodes with simultaneous resource possession, with a view to calculating call blocking probabilities. The queueing network is analyzed by decomposition using a modified version of Courtois' algorithm. Numerical comparisons of the decomposition algorithm against simulation show that the algorithm has good accuracy. Also, it is shown that the proposed algorithm is an improvement over the well-known single-node decomposition algorithm based on the link-independence assumption.

An algorithm to compute blocking probabilities in multi-rate multi-class multi-resource loss models

In this paper we consider a family of product-form loss models, including loss networks (or circuit-switched communication networks) and a class of resource-sharing models. There can be multiple classes of requests for multiple resources. Requests arrive according to independent Poisson processes. The requests can be for multiple units in each resource (the multi-rate case, e.g. several circuits on a trunk). There can be upper-limit and guaranteed-minimum sharing policies as well as the standard complete-sharing policy. If all the requirements of a request cannot be met upon arrival, then the request is blocked and lost. We develop an algorithm for computing the (exact) steady-state blocking probability of each class and other steady state descriptions in these loss models. The algorithm is based on numerically inverting generating functions of the normalization constants. In a previous paper we introduced this approach to product-form models and developed a full algorithm for a class of closed queueing networks. The inversion algorithm promises to be even more useful for loss models than for closed queueing networks because fewer alternative algorithms are available for loss models. Indeed, for many loss models with sharing policies other than traditional complete sharing, our algorithm is the first effective algorithm. Unlike some recursive algorithms, our algorithm has a low storage requirement. To treat the loss models here, we derive the generating functions of the normalization constants and develop a new scaling algorithm especially tailored to the loss models. In general, the computational complexity grows exponentially in the number of resources, but the computation can often be reduced dramatically by exploiting conditional decomposition based on special structure and by appropriately truncating large finite sums. We illustrate our numerical inversion algorithm by applying it to several examples. To validate our algorithm on small models, we also develop a direct algorithm. The direct algorithm itself is of interest, because it tends to be more efficient when the number of resources is large, but the number of request classes is small. Furthermore, it also allows a form of conditional decomposition based on special structure.

Blocking probabilities for large multirate erlang loss systems

This paper is concerned with the computation of asymptotic blocking probabilities for a generalized Erlangian system which results when M independent Poisson streams of traffic with rates access a trunk group of C circuits with traffic from stream k requiring Ak circuits which are simultaneously held and released after a time which is randomly distributed with unit mean and independent of earlier arrivals and holding times. A call from stream k is lost if on arrival less than Ak circuits are available. Although exact expressions for the blocking probabilities are known, their computation is unwieldy for even moderate-sized switches. It is shown that as the size of the switch increases in that both the traffic rates and trunk capacity are scaled together, simple asymptotic expressions for the blocking probabilities are obtained. In particular the expression is different for light, moderate and heavy loads. The approach is via exponential centering and large deviations and provides a unified framework for the analysis.