Dimitris Logothetis

Efficient computation of delay-sensitive routes from one source to all destinations

In this paper we describe an efficient algorithm for the constrained shortest path problem which is defined as follows. Given a directed graph with two weights on each link e, a cost l/sub e/, and a delay t/sub e/, find the cheapest path from a source to all destinations such that the delay of each path is no more than a given threshold. The constrained shortest path problem arises in quality-of-service-sensitive routing in data networks and is of particular importance in real time services. The problem formulation and the algorithmic framework presented are quite general; they apply to IP, ATM, and optical networks. Unlike previous algorithms, our algorithm generates paths from one source to all destinations. Our algorithm is strongly polynomial, and is asymptotically faster than earlier algorithms. We corroborate our analysis by a preliminary simulation study.

Transient analysis of Markov regenerative stochastic Petri nets: a comparison of approaches

We present and compare two different approaches for the transient solution of Markov regenerative stochastic Petri Nets: the method based on Markov regenerative theory and the method of supplementary variables. In both cases the equations that govern the marking process of the non-Markovian stochastic Petri net are presented and then solved either in time-domain or using a Laplace-Stieltjes transformation. Then a comparison of both approaches is presented: expressions for asymptotic computational costs and storage requirements are developed and experimental studies are performed to compare accuracy, time, and space complexity.

Performance modeling of wireless networks with generally distributed handoff interarrival times

Handoff is an important issue in cellular mobile telephone systems. Recently, studies that question the validity of the assumption of handoff arrivals being Poissonian have appeared in the literature. The reasoning behind this claim can be summarized as follows: even if the new call arrival process is assumed to be Poisson, the handoff process due to dependencies with neighboring cells, call blocking and other reasons is not necessarily Poisson. The above-mentioned fact mandates the need to consider more general performance models that allow for arbitrarily distributed interarrival times. In this paper we provide numerical solutions for new and handoff call blocking probabilities with arbitrary handoff interarrival time distribution. For this purpose, we first prove that the underlying stochastic process is a Markov regenerative process and subsequently we use their mathematical theory to develop numerical techniques for important Quality of Service measures. Our results can be seen as a generalization of the recent work by Haring et al. [IEEE Trans. Vehi. Technol. 50 (2001) 664] where handoff traffic was assumed to form a Poisson process. Our work can be used for more accurate dimensioning of cellular systems with realistic traffic.

Markov regenerative models

The Markov Regenerative Stochastic Process (MRGP) has been shown to capture the behavior of real systems with both deterministic and exponentially distributed event times. In this paper we survey the MRGP literature and focus on the different solution techniques that can be adopted for their transient analysis. We also discuss the automated generation of MRGPs from deterministic and stochastic Petri nets (DSPNs). Some examples are developed and solved to illustrate the modeling power of MRGPs and DSPNs.<<ETX>>

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).

Analysis of a polling system for telephony traffic with application to wireless LANs

Recently, polling has been included as a resource sharing mechanism in the medium access control (MAC) protocol of several communication systems, such as the IEEE 802.11 wireless local area network, primarily to support real-time traffic. Furthermore, to allow these communication systems to support multimedia traffic, the polling scheme often coexists with other MAC schemes such as random access. Motivated by these systems, we develop a model for a polling system with vacations, where the vacations represent the time periods in which the resource sharing mechanism used is a non-polling mode. The real-time traffic served by the polling mode in our study is telephony. We use an on-off Markov modulated fluid (MMF) model to characterize telephony sources. Our analytical study and a counterpart validating simulation study show the following. Since voice codec rates are much smaller than link transmission rates, the queueing delay that arises from waiting for a poll dominates the total delay experienced by a voice packet. To keep delays low, the number of telephone calls that can be admitted must be chosen carefully according to delay tolerance, loss tolerance, codec rates, protocol overheads and the amount of bandwidth allocated to the polling mode. The effect of statistical multiplexing gain obtained by exploiting the on-off characteristics of telephony traffic is more noticeable when the impact of polling overhead is small

Transient analysis of the leaky bucket rate control scheme under Poisson and ON-OFF sources

Derives expressions for the time-dependent state probabilities and the time-averaged state-probabilities for the leaky bucket rate control scheme. The model is based on the theory of Markov regenerative processes. The results specialize to those obtained by Sidi et al. (1993) for the steady-state behavior of the leaky bucket. The present results are more general, however, in that they apply to the transient regime and to more general arrival processes.<<ETX>>

The Effect of Detection and Restoration Times forError Recovery in Communication Networks

Detection and restoration times are oftenignored when modeling network reliability. In thispaper, we develop Markov Regenerative Reward Models(MRRM) to capture the effects of detection andrestoration phases of network recovery. States of the MRRMrepresent conditions of network resources, while statetransitions represent occurrences of failure, repair,detection, and restoration. Reward rates, assigned to states of the MRRM are computed based on aperformance model that accounts for contention. Wecompare our model with ones that ignore these parametersand show significant differences, in particular for transient measures.

Time-Dependent Behavior of Redundant Systems with Deterministic Repair

In this paper, we consider various redundant systems attended by a single repairperson that services components in a First Come First Served (FCFS) order. Failure times are taken to be exponentially distributed random variables, while repair times are deterministic. As a result, the underlying stochastic process is not Markovian or semi-Markovian. However, the underlying stochastic process is Markov regenerative and as such we are able to write and solve equations for the process. We compute various dependability measures, such as reliability function, Mean Time To Failure (MTTF), time-dependent and steady-state availability.

Reliability analysis of the double counter-rotating ring with concentrator attachments

The inherently weak reliability behavior of the ring architecture has led network designers to consider various design choices to improve network reliability. We assess the impact of provisions such as node bypass, secondary ring and concentrator trees on network reliability. For this reason, we develop closed-form expressions for the reliability and the mean time-to-failure of the double counter-rotating ring architecture. For our comparisons we adopt the 2-terminal, and the all-terminal reliability criteria. Our network reliability expressions are valid for any time-to-failure distributions of links and nodes. >