singlequeuemultiserver

Single queue multi-server, often described as a single-queue multi-server system, is a classic queueing structure in which customers form one waiting line that feeds multiple parallel servers. This arrangement is commonly analyzed as models like M/M/c or M/G/c with a first-come, first-served discipline. Key parameters include the arrival rate λ, the service rate μ of each server, and the number of servers c, with system stability requiring ρ = λ/(c μ) < 1.

In an M/M/c FCFS system, performance metrics include the probability that an arriving customer must wait (often treated via the Erlang-C formula), the average waiting time in queue Wq, the total time in the system W, and the average numbers in queue Lq and in the system L. A commonly used relation is Wq = Pw / (c μ − λ), where Pw is the probability of waiting derived from the Erlang-C expression. These metrics provide a baseline for evaluating service levels and staffing.

Advantages of a single queue include efficient utilization of all servers through pooling, typically shorter and more predictable waits than multiple separate queues, and a simplified customer experience. Disadvantages can include sensitivity to variability in arrival and service patterns and potential bottlenecks if demand approaches capacity, since a single queue feeds all servers.

Applications span call centers, service desks, cloud computing and load-balanced computing farms, printing networks, and other settings where multiple servers can serve customers but a single, shared waiting line promotes fairness and efficiency. Design considerations focus on selecting an appropriate number of servers, accounting for service-time variability, and deciding whether FCFS is optimal or if priority or batching rules are warranted.