Convexity properties of the Erlang loss formula

A Harel - Operations Research, 1990 - pubsonline.informs.org
We prove that the throughput of the M/G/x/x system is jointly concave in the arrival and service
rates. We also show that the fraction of customers lost in the M/G/x/x system is convex in …

Sharp bounds and simple approximations for the Erlang delay and loss formulas

A Harel - Management Science, 1988 - pubsonline.informs.org
Some sharp bounds and simple approximations are obtained for the Erlang delay formula
and for the Erlang loss formula. One of the results is then used to get a simple analytical …

Forecasting stock prices

A Harel, G Harpaz - International Review of Economics & Finance, 2021 - Elsevier
We apply concepts form machine learning to forecast stock prices. First, we introduce the
general (3 by 3) forecasting model, in which the financial markets are populated by three types …

Strong convexity results for queueing systems

A Harel, PH Zipkin - Operations Research, 1987 - pubsonline.informs.org
We prove a strong (and seemingly odd) result about the M/M/c queue: the reciprocal of the
average sojourn time is a concave function of the traffic intensity. We use this result to show …

Sharp and simple bounds for the Erlang delay and loss formulae

A Harel - Queueing Systems, 2010 - Springer
We prove some simple and sharp lower and upper bounds for the Erlang delay and loss
formulae and for the number of servers that invert the Erlang delay and loss formulae. We also …

Alternative utility functions: review, analysis and comparison

A Harel, JC Francis, G Harpaz - Review of Quantitative Finance and …, 2018 - Springer
The paper reviews the development of von Neumann and Morgenstern (vNM) utility theory.
Kahneman and Tversky’s (KT’s) prospect theory is introduced. The vNM utility function is …

The convexity of a general performance measure for multiserver queues

A Harel, P Zipkin - Journal of Applied Probability, 1987 - cambridge.org
This paper examines a general performance measure for queueing systems. This criterion
reflects both the mean and the variance of sojourn times; the standard deviation is a special …

Convexity results for single-server queues and for multiserver queues with constant service times

A Harel - Journal of applied probability, 1990 - cambridge.org
We show that the waiting time in queue and the sojourn time of every customer in the G/G/1
and G/D/c queue are jointly convex in mean interarrival time and mean service time, and …

Convexity results for the Erlang delay and loss formulae when the server utilization is held constant

A Harel - Operations research, 2011 - pubsonline.informs.org
This paper proves a long-standing conjecture regarding the optimal design of the M/M/s
queue. The classical Erlang delay formula is shown to be a convex function of the number of …

Polling, greedy and horizon servers on a circle

A Harel, A Stulman - Operations research, 1995 - pubsonline.informs.org
Service in a loop-based polling system consists of a single server moving around a closed
tour, stopping to perform services wherever requests are encountered. There are N stations (…