Blockchain facilitates a broad spectrum of applications such as transaction of cryptocurrency, catering to financial services, designing and constructing smart cities and so on. It has astounding benefits including accountability, consistency and decentralization. Smart healthcare can be exemplified as utilizing propitious electronic technology safeguarded with blockchain for superior diagnosis of the disorders, improvised and cost-effective treatment of the patients, and enhanced quality of lives. Since, blockchain in smart healthcare architecture hosts substantial amount of patient data queueing models play a pivotal role to efficiently process the data. In this paper, it highlights the concepts of blockchain, then delve into the smart healthcare architecture and then deal with the several queueing models that already exist. It proposes the model i.e. hQChain which is inculcating M1,b/Mb/1 queueing model into blockchain based smart healthcare architecture. It offers a queuing mathematical and analytical model to analyze and study the performance measurement of hQChain model.