TANDEM QUEUES WITH DEPENDENT SERVICE TIMES IN LIGHT TRAFFIC

Light traffic results about delay in queue are obtained for r single-channel queues in tandem with Poisson arrivals where the r service times of the same customer at different stations have an arbitrary joint distribution. By light traffic is meant asymptotic behavior as server utilization approaches zero. A detailed analysis of delay at the second station is presented for r equals 2. An expression for expected delay is obtained for r equals 3. Methods developed for these purposes may be used for arbitrary r greater than 3. For arbitrary r, an expression for expected delay is obtained in the special case where the r service times of the same customer are equal. For exponential service, a simple closed form expression is obtained. For r equals 2, it is shown that when service times are positively quadrant dependent, expected delay is greater than when service times are independent.