The G/G/1 queue

The notation G/G/1 queue is usually referred to a single-server queue with first-in-first-out discipline and with a general distribution of the sequences of inter-arrival and service times (which are the “driving sequences” of the system). Customers are numbered n = 0, 1, . . .. We assume that customer 0 arrives to a system at time t = 0 and finds there an initial amount of work, so has to wait for W0 ≥ 0 units of time for the start of its service. Let tn be the time between the arrivals of nth and (n + 1)st customers and sn the service time of the nth customer. Let Wn be the waiting time (delay) of the nth customer, i.e. time between its arrival and beginning of its service. Then, for n ≥ 0, the sequence {Wn} satisfies Lindley’s equations Wn+1 = (Wn + sn − tn) (1)