The E-commerce zone is crowded with many Internet users. Medical E-commerce has had significant growth in part because of a great deal of growth in the Indian E-commerce field. Medical E-commerce sites use cloud computing to guarantee a high quality of service anywhere and anytime in the world. For online access, the customer's expectations are very high. Medical E-commerce retailers are directed towards cloud service providers based on their quality of service. During online shopping, impatient customers may abandon a specific medical E-commerce shopping cart due to slow response. This is quite difficult to endure for a medical E-commerce firm. The research described herein observed the effect of shopping cart abandonment on medical E-commerce websites deployed in cloud computing. The impact of the idle virtual machine on customer impatience during medical E-commerce shopping was also studied. The ultimate aim of this study was to propose a stochastic queueing model and to yield results through probability generating functions. The results of the model may be highly useful for a medical E-commerce firm facing customer impatience, so as to design its service system to offer satisfactory quality of service. © 2017