Allocation of Waiting Time by Trading in Position on a G/M/S Queue

Customers on an S-server queue with exponential service times face losses due to waiting that are proportional to waiting time, with different loss rates. Customers are otherwise identical. They have complete knowledge of each other's loss rates. Instead of bribing a queue manager for priority assignment, they buy and sell queue positions among themselves. It is shown that the resulting market in queue positions optimally allocates waiting time. The transactions that can occur are completely characterized, including balking and reneging rules.