A queueing model for crowdsourcing
本文提出一个多服务器排队模型，模拟众包中两类顾客的交互服务过程，并利用矩阵分析法推导稳态下的等待时间分布，为众包平台的服务设计提供参考。
Crowdsourcing is getting popular after a number of industries such as food, consumer products, hotels, electronics, and other large retailers bought into this idea of serving customers. In this paper, we introduce a multi-server queueing model in the context of crowdsourcing. We assume that two types, say, Type 1 and Type 2, of customers arrive to a c-server queueing system. A Type 1 customer has to receive service by one of c servers while a Type 2 customer may be served by a Type 1 customer who is available to act as a server soon after getting a service or by one of c servers. We assume that a Type 1 customer will be available for serving a Type 2 customer (provided there is at least one Type 2 customer waiting in the queue at the time of the service completion of that Type 1 customer) with probability . With probability , a Type 1 customer will opt out of serving a Type 2 customer provided there is at least one Type 2 customer waiting in the system. Upon completion of a service a free server will offer service to a Type 1 customer on an FCFS basis; however, if there are no Type 1 customers waiting in the system, the server will serve a Type 2 customer if there is one present in the queue. If a Type 1 customer decides to serve a Type 2 customer, for our analysis purposes that Type 2 customer will be removed from the system as Type 1 customer will leave the system with that Type 2 customer. Under the assumption of exponential services for both types of customers we study the model in steady state using matrix analytic methods and establish some results including explicit ones for the waiting time distributions. Some illustrative numerical examples are presented.