Learn in the textbookApplications of Discrete Mathematics (Queuing and Optimization)
DefinitionA queue (待ち行列), in the sense of a waiting line, is a model that treats a line waiting its turn for service in numerical terms, based on how arrivals come in and how they are served.
ExplanationBoth the gaps between arrivals and the time needed to serve each one vary, so the average wait and line length are estimated with probability and statistics. The basic form has a single counter that serves arrivals first come, first served. The share of time the counter is busy is called utilization, and it is found by dividing the average service time by the average interarrival time.
AnalogyLike taking a number at a clinic's front desk and sitting in the waiting room until it is called. On busy days, both the crowd in the waiting room and the wait itself grow.
Memory hookQueuing theory began with research into how congested telephone exchange lines would get.