A Fuzzy Erlang Loss Model for Capacity-Limited Electric Vehicle Charging Stations: α-Cut Blocking Analysis and Robust Charger Dimensioning

Abstract

Some charging sites, such as a fixed set of bays at a depot, a parking facility or a roadside plaza, cannot hold a waiting line: a vehicle that finds every charger occupied leaves and is lost. The natural idealisation is the Erlang loss system, whose key quantity is the blocking probability. Its inputs, the arrival rate and the charging rate, are seldom known exactly. This paper treats them as triangular fuzzy numbers and studies the resulting fuzzy blocking probability, together with throughput, lost-vehicle rate and charger utilisation, through α-cuts. Using an inverse representation of the Erlang-B formula, we prove that blocking is strictly increasing in the offered load and strictly decreasing in the number of chargers, and that the exact α-cut of the fuzzy blocking probability is obtained by evaluating the formula at the corners (λ_L, µ_U) and (λ_U, µ_L) of the parameter box, whereas throughput requires the opposite corner pairing. We then define a robust charger count c^*(ε, α) that meets a blocking target for every parameter value at level α, and prove that it exists, is monotone in ε and in α, and satisfies explicit lower and upper bounds. In an illustrative station (hypothetical data, not field measurements) the most-likely and worst-case dimensioning decisions differ by one or two chargers, a difference invisible to a crisp analysis. At full membership every result reduces to the classical Erlang-B model.