This paper investigates the routing problem of a patrolling unit in a distributed service network. The objective is to determine an optimal routing so that response time to service call in a distributed network can be optimized. A node-arc network is presented to model problem with nodes representing the location of clients while arcs length the travel time between nodes. Applying an analysis on the expected maximum response times on each arc to all nodes, we re-model the problem into a new node-arc network with arc lengths are measured in expected maximum response time. A mathematical model is then applied to select the best route minimizing the expected maximum response time of the whole system. The mathematical model can be easily formulated and implemented in commonly available package.