May 23, 2018

September 17, 2005
Carleton Applied Probability Day

Carleton University, Ottawa

Speaker Abstracts

  • Barbara Gonzalez, Mathematics Department, University of Louisiana at Lafayette

    Modeling teletraffic arrivals by a Poisson cluster process.(.pdf format)

    In this paper we consider a Poisson cluster process $N$ as a generating process for the arrivals of packets to a server. This process generalizes in a more realistic way the infinite source Poisson model which has been used for modeling teletraffic for a long time. At each Poisson point $\Gamma_j$,a flow of packets is initiated which is modeled as a partial iid sum process $\Gamma_j+\sum_{i=1}^kX_{ji}$, $k\le K_j$,with a random limit $K_j$ which is independent of $(X_{ji})$ and the underlying Poisson points $(\Gamma_j)$. We study the covariance structure of the increment process of $N$. In particular, the covariance function of the increment process is not summable if the right tail $P(K_j>x)$ is regularly varying with index $\alpha\in (1,2)$, the distribution of the $X_{ji}$'s being irrelevant. This means that the increment process exhibits long-range dependence. If ${\rm var}(K_j)<\infty$ long-range dependence is excluded. We study the asymptotic behavior of the process $(N(t))_{t\ge 0}$ and give conditions on the distribution of $K_j$ and $X_{ji}$ under which the random sums $\sum_{i=1}^{K_j}X_{ji}$ have a regularly varying tail. Using the form of the distribution of the interarrival times of the process $N$ under the Palm distribution, we also conduct an exploratory statistical analysis of simulated data and of Internet packet arrivals to a server. We illustrate how the theoretical results can be used to detect distributional characteristics of $K_j$, $X_{ji}$, and of the Poisson process.

  • Haipeng Shen, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill

    A Queueing-Science Look at a Telephone Call Center
    A call center is a service network in which agents provide telephone-based services. Customers that seek these services are delayed in tele-queues. This talk summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year.

    We look at call centers through the perspective of queueing science, which combines mathematically elegant queueing theory with empirically data-driven statistical analys. The service process is decomposed into three fundamental
    components: arrivals, customer patience, and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. The talk then surveys how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations.

    The papers associated with this talk are downloadable at

  • Wojciech Szpankowski, Department of Computer Science, Purdue University

    Analytic Algorithmics, Combinatorics and Information Theory
    Analytic information theory aims at studying problems of information theory using analytic techniques of computer science and combinatorics. Following Hadamard's and Knuth's precept, we tackle these problems by complex analysis methods such as generating functions, Mellin transform, Fourier series, saddle point method, analytic poissonization and depoissonization, and singularity analysis. This approach lies at the crossroad of computer science and information theory. In this talk, we concentrate on one facet of information theory (i.e., source coding better known as data compression), namely the redundancy rate problem and types. The redundancy rate problem for a class of sources is the determination of how far the actual code length exceeds the optimal (ideal) code length. The method of types is a powerful technique in information theory, large deviations, and analysis of algorithms. It reduces calculations of the probability of rare events to a combinatorial analysis. Two sequences are of the same type if they have the same empirical distribution. We shall argue that counting types can be accomplished efficiently by enumerating Eulerian paths (Markov types) or binary trees with a given path length (universal types). On the other hand, analysis of the redundancy rate problem for memoryless and Markov sources leads us to tree generating functions (e.g., arising in counting labeled rooted trees) studied extensively in computer science.

  • Damon Wischik, Department of Computer Science University College London (UCL)

    Queueing theory for TCP/IP
    The current Internet is not very good for transferring large files at high speeds, nor for transmitting live audio and video. This is not because of hardware limitations; it is because of problems with the architecture of the Internet, and especially with TCP, the algorithm for controlling congestion, implemented in every computer on the Internet.

    TCP controls congestion by adjusting the transmission rate of a traffic flow in response to the congestion it perceives in the network. Queueing theorists, on the other hand, are used to using traffic models which do not respond to congestion. For example, queueing theorists are used to the idea that the larger the buffer the less likely it is to overflow. But TCP thinks that the absence of overflow means the network is underutilized, and so it increases its transmission rate until the buffer overflows, no matter how large it is.

    In this talk I will describe some recent work on queueing theory for TCP. This theory uses the predictability of aggregate traffic flows, both at a fluid level and a stochastic level. The theory suggests ways to enhance TCP and build cheaper Internet routers.

    For further information,