Behavior of queues at signalized intersections in heavy traffic
This paper derives the asymptotic behavior of traffic queues at signalized intersections when the excess of departure capacity over arrivals approaches zero from above. The most interesting result is that the distribution of queue length approaches a negative exponential, with fewer restrictive assumptions than hitherto known. The main improvement results from more precise use of a combinatorial lemma of Spitzer, giving the maximum of the partial sums of a sequence of independent identically distributed random variables, plus some specific constructive probability calculations, many of them involving the Fourier transform. New results are presented on the probability that the queue be below a fixed bound and/or on the probability that the queue be empty. Applications to on-line estimators for real-time traffic control are suggested.