Heavy traffic analysis of polling systems in tandem

We analyze the performance of a tandem queueing network populated by two customer types. The interarrival times of each type and the service times of each type at each station are independent random variables with general distributions, but the load on each station is assumed to be identical. A setup time is incurred when a server switches from one customer type to the other, and each server employs an exhaustive polling scheme. We conjecture that: a time scale decomposition, which is known to occur at the first station under heavy traffic conditions, holds for the entire tandem system, and we employ heavy traffic approximations to compute the sojourn time distribution for a customer that arrives to find the network in a particular state. When setup times are zero (except perhaps at the first station) and additional "product-form" type assumptions are imposed, we find the steady-state sojourn time distribution for each customer type.