I. Viniotis

Exact Methods for the Transient Analysis of Nonhomogeneous Continuous Time Markov Chains

Most common performance and reliability models assume that rates associated with events such as arrivals, service completions, failures, repairs, etc. are all constant in time. Many practical systems, however, require time- (age-) dependent rates. For example, the use of Weibull failure rates is quite common in many reliability models. Likewise, most actual local area network (LAN) systems experience surges in the number of users that vary in magnitude over time. These surges may often be approximated by a periodic process. Therefore, nonhomogeneous continuous time Markov chains (CTMCs) may be well suited to model such systems. The transient analysis of time-varying linear systems is highly advanced in the field of systems and control theory. We present a review of some useful results, and then apply them to the analysis of nonhomogeneous CTMCs (especially periodic ones). One of the results of this analysis is, that for a certain class of useful nonhomogeneous CTMCs, a very simple method exists for transforming such a CTMC (and not just a periodic one) to an equivalent homogeneous CTMC that is then amenable to such homogeneous methods as Jensen’s method (also known as uniformization or randomization).

Transient behavior of ATM networks under overloads

We characterize the time-dependent behavior of a typical queuing system that arise in ATM networks under the presence of overloads. The transient queue length distribution and transient cell loss probability are obtained numerically and transient characteristics such as maximum overshoot and relaxation time are used to quantify the effects of congestion periods. A new measure, expected excess loss in overload (EELO) is defined to quantify the effects of overload when compared with the system behavior in the steady-state regime. The basic modeling technology that we use is an extended form of stochastic Petri nets and a software tool called the stochastic Petri net package (SPNP).

Adaptive polling schemes for an ATM bus with bursty arrivals

Abstract We consider a high speed ATM bus, which can serve a small number of stations (≤16). The bus is slotted and each slot is long enough to contain one ATM cell. Transmission on the bus is controlled by an arbitrator. Each station sends its status information to the arbitrator at regular intervals. Based on this information the arbitrator makes polling decisions. Due to transmission and processing times the arbitrator makes decisions based on status information which is a few bus slots old. In this paper, we propose adaptive polling schemes assuming bursty arrivals. The schemes take into account both the cell loss probability and the mean waiting times. The advantage of these new schemes over ordinary polling is also demonstrated.

A parallel router architecture for high speed LAN internetworking

A parallel router architecture for processing network-layer protocols at FDDI (fiber distributed data interface) speeds is proposed. At high speeds the computing power of existing routers becomes the performance bottleneck (for processing small frame sizes). Hence, a completely different approach is required in designing a router. The opportunities of parallel processing in a network protocol are investigated. Several levels of parallel processing are considered, and an architecture for the most practical and feasible approach is proposed. The concept of a snoopy header cache is introduced. Algorithms for reducing the mean processing delay by balancing the load among the processors are discussed. The performance of the router is evaluated by analytic methods and is compared with simulation results. The results from both the analytic model and the simulator reinforce the choice of a header cache in a multiprocessor environment.<<ETX>>

A novel architecture and flow control scheme for private ATM networks

The primary performance measures used to evaluate any congestion control algorithm applicable to ATM networks are, the utilization achieved and the guaranteed packet loss or the Grade of Service (GOS). In any scheme where the sources are controlled there has to be a compromise between the throughput and the GOS, introduced due to the burstiness of the sources. This trade-off can be reduced by the effective use of buffers along with a fair and adaptive flow control scheme. This paper proposes such a scheme, including a node architecture with an off-line shared buffer. In combination with this architecture a threshold controlled, backward notification flow control algorithm is introduced. The off-line buffer is used to absorb reasonable sized overloads, thus increasing the utilization of resources. Extended overloads generate control messages and are flow controlled, thus avoiding unacceptable degradation in the GOS. Flow control messages are relayed back only if the source is truly violating. Hence the proposed scheme is fair and precludes flooding of the network with control messages and the possibility of oscillation in reporting the network status. The issues surrounding this scheme are discussed and possibilities of further research are presented. A simulation model with some results are provided to support our claims.

Virtual path assignment in atm networks

In this thesis, we address the problem of assigning virtual paths in Asynchronous Transfer Mode (ATM) networks. Virtual Path (VP) Assignment is an important resource and traffic management activity in ATM networks. By using the VP concept, the logical layout of the network can be administered to minimize the total network cost to the provider and to achieve specified quality of service (QoS) for users. We formulate the VP Assignment problem as a constrained optimization problem; the objective function to be minimized reflects processing/control costs at nodes and transmission costs between nodes. The blocking probability quality of service (QoS) requirements and overall throughput of the network are taken into consideration in the solution process as constraints. Since the solution space is complex, we first develop a deterministic, iterative heuristic algorithm (VPA-F) to reach a “near-optimal” VP configuration for a given physical network and traffic demand with fixed-routes. The VPA-F algorithm assumes that connection routes in the physical network are given. The Multi-Rate Loss Network model is used in the calculation of connection-level blocking probabilities. An innovative VP capacity allocation procedure is designed based on max-min fairness principle in order to meet the accuracy and computation-time goals. The heuristic algorithm is expanded to include the assignment of variable connection routes. The connection routing is incorporated into the optimization algorithm (VPA) by applying a rerouting heuristic for traffic streams. Results of runs of the VPA-F algorithm are presented, for various forms of the objective function and constraints. The minimum number of VP hops objective is found to be the most suitable for a fixed capacity network. The VPA algorithm (with variable connection routing) is tested with this objective function, and its performance is compared to VPA-F.

Buffer sizing for ABR traffic in an ATM switch

The B-ISDN will carry a variety of traffic types: the variable bit rate traffic (VBR), of which compressed video is an example, continuous bit rate traffic (CBR), of which telemetry is an example, data traffic, and available bit rate traffic (ABR) that represents aggregate data traffic with very limited guarantees on quality. The authors consider the VBR, data and ABR traffic types and obtain the cumulative distribution function (cdf) of the queueing delay experienced by a burst of ABR traffic in the output buffer of an ATM switch. The size of the ABR buffer is an important design parameter and the authors use the cdf to predict this value. They develop a stochastic Petri net model assuming periodic burst arrivals for VBR and Markovian arrival processes for data and ABR, and using a decomposition approach, solve the model numerically.

Priority-based dynamic access policies to WAN from LAN/MAN

The authors consider the integration problem of LAN/MAN traffic to WAN by ATM/SONET multiplexing. They propose separate buffers for voice and data to efficiently control the throughput of each traffic type. Transmission bandwidth is dynamically and adaptively shared between voice and data to guarantee grade of service (GOS) requirements for each traffic type. The authors propose two algorithms for access policies; the (N/sub 1/,N/sub 2/) scheme and its adaptive variation. Their algorithms do not require the knowledge of arrival statistics. In the fact scheme, they can play with the tradeoff between delay and cell loss probability of each traffic type. In the second scheme, for most of the time and under normal network conditions, voice traffic has higher priority. Data traffic has higher priority when the number of data cells queued reaches a certain threshold. They show how the network performance is affected by several system parameters.<<ETX>>

Optimal Resource Scheduling in Wireless Multiservice Systems with Random Channel Connectivity

We investigate an optimal scheduling problem in a discrete-time system of L parallel queues that are served by K identical servers. This model has been widely used in studies of emerging 3G/4G wireless systems. We introduce the class of Most Balancing (MB) policies and provide their mathematical characterization. We prove that MB policies are optimal among all work conserving policies; we define optimality as minimization, in stochastic ordering sense, of a range of cost functions of the queue lengths, including the process of total number of packets in the system. We use dynamic coupling arguments for our proof. We also introduce the Least Connected Server First/Longest Connected Queue (LCSF/LCQ) policy as an approximate implementation of MB policies. We conduct a simulation study to compare the performance of several work conserving policies to that of the optimal one. In the simulations we relax some of the mathematical assumptions we required for the analytical proofs. The simulation results show that: (a) in all cases, MB policies outperform the other policies, (b) randomized policies perform fairly close to the optimal one, and, (c) the performance advantage of the optimal policy over the other work conserving policies increases as the channel connectivity decreases.

Achievability of combined GOS requirements in broadband networks

Conservation laws to investigate the achievability of performance objectives in broadband networks are developed. Conservation laws for delay presented so far assumed infinite buffer size. No conservation laws for delay with finite buffer were established. In the present work, it is shown that the conservation law for combining scheduling and pushout mechanisms is represented as a two-dimensional region, rather than as a line, in the two-dimensional plane. In this case, the classical mixing strategies of E. Gelenbe and I. Mitrani (1980) may not be used to achieve the performance objectives. Therefore, there is a need for some other control strategies in order to satisfy both delay and loss performance objectives. On the basis of these conservation laws, the authors provide a dynamic queueing discipline that achieves the specified objectives, if the objectives can be satisfied, and treats the various workload classes fairly, if they cannot.<<ETX>>