Sojourn times in finite-capacity processor-sharing queues

• Published in: 2005 Next Generation Internet Networks pp. 53 - 60
• Main Authors: Borst, S., Boxma, O., Hegde, N.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2005
• Subjects: Data systems; Delay; Fluctuations; Laplace equations; Mathematics; Multiaccess communication; Numerical analysis; Scheduling algorithm; Throughput; Time measurement
• ISBN: 9780780389007; 078038900X
• DOI: 10.1109/NGI.2005.1431647

Motivated by the need to develop simple parsimonious models for evaluating the performance of wireless data systems, we consider finite-capacity processor-sharing systems. For such systems, we analyze the sojourn time distribution, which presents a useful measure for the transfer delay of documents such as Web pages. The service rates are allowed to be state-dependent, to capture the fact that the throughput in wireless data systems may vary with the number of active users due to scheduling gains or channel collisions. We derive a set of linear equations for the Laplace-Stieltjes transforms of the sojourn time distributions, conditioned on the number of users upon arrival. This set of equations is solved, and the resulting LST's are inverted, resulting in a phase-type distribution for the unconditional sojourn time. Numerical results are provided, and two types of approximations are proposed that substantially reduce the computational effort.