An efficient control of emergency response units can greatly reduce injuries and adverse impacts. One way to enhance performance is applying a mobile facility concept , instead of a fixed facility. Once an emergency response unit is assigned to an incident, the remaining emergency vehicles can be relocated to better respond to future incidents.
Traditional models need input frequency of requests given in advance to get approximate answers. For example, Mirchandani and Odoni  assumes that a given number of independent and identically distributed (IID) events occur over a time interval. However, the sequence is an ordered combination (permutation) of emergency requests. Suppose a set of sequences with the past request at site (2), current request at site (3), and next requests at either site 1 or site 2. Let the probability of incident at site 1 is 10% and at site 2 is 90%. Traditional approach neglects three essential properties. First, without consideration of the order, the dispatcher would make a decision based on the anticipation of an incident at site 2. This will lead to excessive response time when an incident occurs at site 1 before site 2. Such scenario will make the site 1 to be served from resources farther away than regularly assigned resources, or will not be addressed until the closest resource becomes available. Without an appropriate help, lack of tools may cause an incident to block the traffic flow and induce inefficiencies in the clearance operation.
Second, with a randomness assumption of the IID sequence, reversible times make solutions of two different sequences the same. However, the assigned probability for each sequence is different when an initial incident provokes additional incidents, which are referred to as secondary incidents , . Even though primary incidents at site 2 provoke secondary incidents at site 1, reverse order (primary incidents at site 1) does not have the same mutual dependency. In reality, the probability distributions of the first and the second sequence are different. This property will cause the probability distribution of solution to be asymmetric.