The Queuing theory is prevalent in a variety of settings, including more technical ones like manufacturing, computer networking, telecommunications, as well as everyday ones like bank counters, post offices, ticket booking sites and public transit systems. One of the major important role is the stock market industry. The primary observable performance parameters for any queuing system are the average size of the system, the length of the line, and the wait times in both the queue and the system. A stock market control chart is a graph used to monitor process evolution as well as to monitor and manage ongoing operations. We introduce the encouraged arrival in stock market control chart. The performance features of the ErlangMarkovian single server encouraged arrival queuing model is derived in this work to define control limits and examine its behaviour. In order to emphasis the uses, we provide the numerical examples and results. Little’s law is also verified.