Queueing Performance with Impatient Customers

customer which exceeds its deadline will either leave the queue without service or stay in the queue to get unsucWe consider the problem of scheduling impatient CUScessful service. One application of this problem is the tomers in a non-preemptive G/GI/1 queue. Every CUStransmission of time-constrained messages over a comtomer has a random deadline to the beginning of its munication channel. These messages have to reach their service. Given the distribution of the customer deadreceivers within a certain time interval of their transmislines (rather than their exact values), a scheduling polsion or they are useless to the receivers and considered icy decides the customer service order and also which lost. Two possible scenarios are often encountered in this customer(s) to reject, since those whose deadlines have kind of queueing system[l]. The first is that the server expired do not leave the queue automatically. Our obof the queue is aware of each customer's deadline. The jective is to find an optimal policy which maximizes the messages whose delay times exceed their deadlines are number of customers served before their deadlines. We discarded without transmission. In the second scenario, show that LIFO (last-in first-out) is an optimal service the Server is only aware of the deadline distribution of order when the deadlines are i.i.d. random variables with the customers. Therefore some server work is useless a concave cumulative distribution function. After anabecause of the expiration of customers' deadlines. For lyzhg the rejection strategy, we claim that there is an example, there may be a delay before a dial tone in an optimal policy in the LIFO-TO (time-out) class, as deoverloaded call processing system. If some people start fined in the paper. For the M/GI/1 queue, we further dialing before a dial tone is heard, the system will not prove that unforced idle times are not allowed under this receive all the digits dialed. However, the call is still prooptimal policy. We also show that the optimal LIFO-TO cessed and an unsuccessful call results[4]. A similar case policy assigns a fixed critical time (i.e., its maximum can arise in dealing with time-critical voice or video cells waiting time) to every customer. When the customer in an ATM (Asynchronous Transfer Mode) network. waiting times are unknown, we show that the optimal policy for a M/M/l queue the When the customers, deadlines are available, the (pushshortest time to extinction (STE) and the shortest time Out) Policy, with a fixed buffer size Among Other * a rejection to extinction with inserted idle time (STEI) were proved to be optimal under certain conditions, These policies this may be applied in determining scheduling and buffer management maximize the fraction of customers served within their policies for critical the cells in an ATM (Asynchronous respective deadlines out of an arrival stream. The results for single server queues can be found in [7], [8] and Transfer Mode) network. [2]. In [13], earlier results are extended to multi-server queues. This paper is devoted to determining the optimal poliSome queueing performance is significantly affected by cies when only the deadline cumulative distribution is the behavior of impatient customers. These customers known. Without knowing the deadline of every specific should be served before their respective deadlines. A customer, the control action is to decide, a t appropriate decision instants, which customer to serve and which 'This work WM supported in part by the National Science Foundation under Nl>R-8909719, and by the New York State customer(s) to reject. The rejection is necessary since Center for Advanced Technology in Teleconununications (CATT), the customers whose deadlines have expired do not leave Polytechnic University, Brooklyn, New York. the queue automatically. Therefore a customer could be