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This paper presents an approximate procedure for computing selected performance characteristics of an urban emergency service system. Based on a recently developed hypercube queuing model, the procedure requires for N servers solution of only N simultaneous equations, rather than 2^N as in the exact model. The procedure relies on the theory of M/M/N queues in which servers are selected randomly and without replacement until the first available (free) server is found. The underlying model is intended for analyzing problems of vehicle location and response district design in urban emergency services, includes interdistrict as well as intradistrict responses, and allows computation of several point-specific as well as area-specific performance measures.