In many companies, legacy systems have been used to serve customers arriving at service counters. The demand of a customer arriving at a counter is divided into R subdemands (SDs). Each SD is processed sequentially by the legacy system. When the final SD service is completed, the customer leaves the counter. On the other hand, Internet users desire that each SD be processed through the Internet without going to a service counter. We note that the applications for operating the web system differ from those of the legacy systems. For that reason, companies might use legacy systems for customers who come to the company through the Internet, without changing those legacy systems' applications. This web system, which is integrated with the legacy system, is called a front-end web system. Suppose that, for the web system, demands are generated according to a Poisson process. Then we show that the loss probability and macrostate distribution for the front-end web system are insensitive with respect to the distribution of the discrete random variable R, aside from the continuous distributions of other uncertain factors, under a restriction.