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The case of the Geo/Geo/1 system in which the service times depend on the interarrival times can be studied using the same idea and techniques as in section 1.2.1. If we define the arrival probability as a and the service time completion probability as b = g(a), it is straightforward to extend the ideas of that section directly. The queueing performance measures such as the mean number in the system, which we now define as E(X(a)) can be written as

and the stability condition given as a < g(a). Since the procedures will be the same, they will not be discussed in this chapter.

Table 1.1. Mean number in system for the three cases

b	EX1	EX2	EX3
0.10	****	0.1100	****
0.20	****	0.2400	****
0.30	****	0.3900	****
0.40	****	0.5600	****
0.50	****	0.7500	****
0.60	****	0.9600	1.2000
0.70	1.3153	1.1900	0.5250
0.75	0.7875	1.3125	0.3750
0.80	0.5236	1.4400	0.2667
0.85	0.3502	1.5725	0.1821
0.90	0.2168	1.7100	0.1125
0.95	0.1032	1.8525	0.0528