The Window Fill Rate with Nonzero Assembly Times: Application to a Battery Swapping Network

One suggestion to overcome the range anxiety of electrical vehicle owners is the use of a network of battery swapping stations. To improve the network’s performance, managers can purchase spares and place them in the network’s stations. The battery allocation problem, therefore, is finding the allocation that optimizes the network’s performance. For the performance measure, we consider the window fill rate, that is, the probability that a customer that enters a swapping station will exit it within a certain time window. For the battery swapping network this time window is defined as the customer’s tolerable wait. In our derivation of the window fill rate formulae, we differ from earlier research in that we assume that the time to remove and install a battery is not negligible. We numerically analyze the battery allocation problem for a hypothetical countrywide application in Israel and demonstrate the importance of estimating correctly customers’ tolerable wait. We find that the window fill rate criterion leads to two classes of stations, those that are assigned spares and those that are not. Additionally, we show the savings attained by reducing the swapping time. Finally, we compare between a balanced and imbalanced system (in terms of customer arrival to the various stations) and show that the advantage of each system crucially depends on the length of the tolerable wait.