A Markov Model Based Study of Waiting Time of a Dynamic Distribution Agent in an Online Food Delivery System

Distribution agents (DAs) play a very important role in the online food delivery system. Usually, a DA joins the queue formed in a restaurant. The food delivery apps are designed in such a way that the DA near the restaurant will receive the order reaching that restaurant. This paper introduces a dynamic distribution agent (DDA) who never joins a queue in the hope of receiving orders from more than one restaurant. Using continuous-time Markov models, we analyze the expected waiting time of the DDA and hence examine whether the above DDA's strategy is profitable or not. We consider two models: first in which both the inter-order time and the inter-service time (food preparation time + delivery time) follow different exponential distributions, second in which these random times follow distinct phase-type distributions. Our numerical study based on real-world data suggest that the strategy of the DDA will succeed depending on the number of DAs in competition and the number of restaurants available.