Summary: The Annals of Applied Probability
2004, Vol. 14, No. 3, 1084­1134
DOI 10.1214/105051604000000233
© Institute of Mathematical Statistics, 2004
SCHEDULING A MULTI CLASS QUEUE WITH MANY
EXPONENTIAL SERVERS: ASYMPTOTIC
OPTIMALITY IN HEAVY TRAFFIC
BY RAMI ATAR,1 AVI MANDELBAUM2 AND MARTIN I. REIMAN
Technion­Israel Institute of Technology, Technion­Israel Institute of Technology
and Bell Labs, Lucent Technologies
We consider the problem of scheduling a queueing system in which many
statistically identical servers cater to several classes of impatient customers.
Service times and impatience clocks are exponential while arrival processes
are renewal. Our cost is an expected cumulative discounted function, linear or
nonlinear, of appropriately normalized performance measures. As a special
case, the cost per unit time can be a function of the number of customers
waiting to be served in each class, the number actually being served, the
abandonment rate, the delay experienced by customers, the number of idling
servers, as well as certain combinations thereof. We study the system in
an asymptotic heavy-traffic regime where the number of servers n and the

Source: Atar, Rami - Department of Electrical Engineering, Technion, Israel Institute of Technology
Mandelbaum, Avishai - Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology

Collections: Engineering; Mathematics