We consider the maximal covering location-allocation problem with multiple servers. The objective is to maximize the population covered, subject to constraints on the number of service centers, total number of servers in all centers, and the average waiting time at each center. Each center operates as an M/M/k queuing system with variable number of servers. The total costs of establishing centers and locating servers should not exceed a predetermined amount. We present a mathematical model for the problem, and propose a heuristic solution procedure with two local search algorithms for improving the solutions. Finally, some computational results are presented.