Capacity expansion for a loss system with exponential demand growth
We study a loss system to forecast the demand for capacity based on the forecast demand for service and a specified service level. A little-used property of the Erlang loss formula allows the linear transformation of demand for service into demand for capacity. Next, given the forecast demand for capacity, we approximate a long-run optimal capacity expansion policy by optimizing over successively longer finite time horizons. Analytical formulas together with regression analysis show the significance of the number of potential customers, frequency and duration of their requests for service, and the specified service level on the demand for capacity. Numerical sensitivity analysis exposes the effects of cost parameters, the demand growth rate and the required rate of return on the optimal time intervals between expansions. Scope and purpose Internet use has grown tremendously over the past few years as businesses, educational institutions, government organizations and individuals have become heavily dependent on its capability for rapid communication and data exchange. As demand continues to grow, reliable access to the Internet will be critical for many users. For Internet service providers (ISPs), providing a high level of service is essential for keeping subscribers in a competitive market. This paper considers a potential busy signal problem in Internet access on a dial-up system due to insufficient capacity at the ISP company. We show how to exploit a linearity property of the Erlang loss formula to determine the capacity that will be required to maintain a specified level of customer service for a given forecast of demand growth. A numerical algorithm determines the optimal time points for the ISP to expand its capacity in order to meet the demand for capacity derived from an exponential growth in subscribers.
capacity expansion loss system erlang loss formula