Recensione dell'articolo:(Fazel-Zarandi, Mohammad M.; Kaplan, Edward H. - "Approximating the first-come, first-served stochastic matching model with Ohm's law." Oper. Res. 66 (2018), no. 5, 1423-1432.) MR3872113 MathSciNet ISSN 2167-5163

In this paper, the authors consider a problem inherent in the first-come first-served (FCFS) matching model. They consider a system with two infinite streams, one of customers and one of servers. Each server must be matched to a single customer of appropriate type. Matching is FCFS in the following sense: the first server in the infinite server stream scans the list of customers sequentially, starting with the first customer on the list, until the first customer eligible to receive service from the scanning server is found. This customer-server pair matches, and leaves the system, and the process repeats with the next server, who again scans the stream of customers, starting with the first customer, on the list. Equivalently, matching can proceed with the first customer in the customer list scanning the list of available servers and matching the first eligible server found. While the stochastic FCFS matching problem is simple to pose, its exact solution is very difficult. In this context the authors study an approximate solution that is simple to compute and highly accurate. Their approximation requires reimagining the customer/server compatibility graph as a circuit network, customer arrival rate as current injections into nodes representing each customer type, server availability rates as current removals from nodes representing each service type, and the matching rates as current flow across the circuit network. The attraction of this approach is that Ohm's Law governs the current flow in circuit networks. This fact leads to an easy-to-solve linear system for approximating the matching rates.