Abstract
We consider the single-server queueing system where successive customers arrive at the epochs t0 (= 0), t1, t2,... and demand services times v1, v2,.... The interarrival times are then given by u n = t n — t n-1 (n≥1). Let Xk = Vk — uk (k ≥ 1), and So = 0, S n = X 1 + X 2 + … + X n (n ≥ 1). We assume that the X kare mutually independent random variables with a common distribution; the basic process underlying this queueing model is the random walk {Sn}. To see this, let Wn be the waiting time of the nth customer and I n the idle period (if any) that just terminates upon the arrival of this customer. Then clearly for n≥ 0
.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Prabhu, N.U. (1998). The Queue GI/G/1. In: Stochastic Storage Processes. Applications of Mathematics, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1742-8_2
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1742-8_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7260-1
Online ISBN: 978-1-4612-1742-8
eBook Packages: Springer Book Archive