Increased Resource Utilization Through Sharing as Analyzed Using a Random Walk with an Absorbing Barrier

Abstract

Intuition supports the idea that if multiple entities use items to service their clients, then sharing the items between the entities will result in more provided services than if the items are pre-allocated to each entity. This idea is quantified by first creating a grid of two to five dimensions (one dimension for each entity). The number of items in use is represented by a single point whose projection on each axis is determined by the number of items in use by each entity. Moving from point to point on this grid occurs as each entity needs an additional item or gives one up. This movement is similar to a Random Walk. The probabilities of moving forward or backward are each independently chosen to represent customer usage. An absorbing barrier enforces the finite number of items available. The results of a computer program simulating this model is presented which shows improved resource utilization. Next, a detailed analysis is developed and the formula obtained is simple and accurate in predicting the results.over the range computed by the simulation.