ABSTRACT

We study a queueing system of an unreliable server providing services to customers with two different service rates. When the system is empty of customers, the server takes a vacation and provides a low service rate. Once the vacation is completed, the server is resumed to serve customers, if any, at a higher service rate, or takes another vacation if the server found an empty system. The server is subject to random breakdowns when serving customers and if failed, it enters a repair stage. Under different system information levels, we investigate customers’ equilibrium strategies and follow-up system measures. Numerical comparisons among different information levels reveal that when the traffic load is large enough, the service provider (SP) prefers to disclose the server’s status and queue length information to customers to maximize the system throughput. While when the traffic load is small enough, there exist two cases with regard to the failure rate: (i) If the failure rate is smaller than a certain threshold, the SP tends to conceal the system information. (ii) If the failure rate is greater than the threshold, revealing the information is helpful to maximize the system throughput.

摘要

我们研究了一种不可靠的服务器的排队系统，该服务器向具有两种不同服务费率的客户提供服务。当系统中没有客户时，服务器将休假并提供较低的服务费率。休假完成后，服务器将以更高的服务费率继续为客户服务（如果有），或者如果服务器发现一个空系统，则再次休假。服务客户时，服务器会随机发生故障，如果发生故障，它将进入维修阶段。在不同的系统信息级别下，我们研究客户的均衡策略和后续系统措施。不同信息级别之间的数值比较表明，当流量负载足够大时，服务提供商（SP）希望向客户公开服务器的状态和队列长度信息，以最大程度地提高系统吞吐量。当业务负载足够小时，关于故障率存在两种情况：（i）如果故障率小于某个阈值，则SP倾向于隐藏系统信息。（ii）如果故障率大于阈值，则显示信息有助于最大化系统吞吐量。