Charles Knessl

Heavy-traffic analysis of a data-handling system with many sources

A model is considered in which a buffer receives messages from N independent and identical information sources that asynchronously alternate between exponentially distributed periods in the “on” and “off” states. While on, a source transmits at unit rate. The buffer depletes through an output channel with a given maximum transmission rate

A Note on a Moving Boundary Problem Arising in the American Put Option

c < N

Integral representations and asymptotic expansions for Shannon and Renyi entropies

. This model is useful for a data-handling switch in a computer network. Anick, Mitra, and Sondhi [Bell System Tech. J., 61 (1982), pp. 1871–1894] have derived an explicit expression for the equilibrium probability

On finite capacity processor-shared queues

G( x )

A QUEUEING SYSTEM WITH QUEUE LENGTH DEPENDENT SERVICE TIMES, WITH APPLICATIONS TO CELL DISCARDING IN ATM NETWORKS

that the buffer content exceeds x, which is convenient for numerical calculations for moderate values of N. In this paper, the heavy traffic case, in which N is large and the system is close to instability, is investigated. Important scalings are introduced, and a two-term asymptotic approximation to

An effective asymptotic formula for the Stieltjes constants

G( x )

Exact and asymptotic solutions to a PDE that arises in time-dependent queues

is derived, with the help of function theoretic techniques. Numerical comparisons are given that show the quality of the approximation.

Asymptotic expansion for large closed queuing networks

We consider an American put option, under the Black-Scholes model. This corresponds to a moving boundary problem for a PDE. We convert the problem to a nonlinear integral equation for the moving boundary, which corresponds to the optimal exercise of the option. We use singular perturbation methods to compute the moving boundary, as well as the full solution to the PDE, in various asymptotic limits. We consider times close to the expiration date, as well as systems where the interest rate is large or small, relative to the volatility of the asset for which the option is sold.

A fork-join queueing model: Diffusion approximation, integral representations and asymptotics

Abstract We derive integral representations for the Shannon and Renyi entropies associated with some simple probability distributions. These include the Poisson, binomial, and negative binomial distributions. Then we obtain full asymptotic expansions for the entropies.

On the transient behavior of the m/m/m/m loss model

A processor-sharing queueing system is considered that can accommodate a finite number K of customers. In a processor-shared queue, every customer gets an equal fraction of the server (processor). The main quantity of interest in such a system is a customer’s response time (time spent in system) conditioned on that customer’s total required service and the number of other customers present at the arrival time. Using singular perturbation methods, we construct asymptotic expansions for the first two moments of the conditional response time for systems where the capacity K is large.