An Application of Queueing Theory to the Relationship Between Insulin Level and Number of Insulin Receptors

Insulin is a hormone that regulates blood glucose levels. Its deficiency or over secretioncause many disorders including polyurea, polydipsia, and weight loss in metabolism.Publications to date show strict relationships between insulin level and number of insulinreceptors in a cell. In this respect a mathematical estimation on insulin level andnumber of insulin receptors may be important in order to understand some diseasesrelated to insulin level and number of insulin receptors. In the present study, a queueingtheory originated model is applied to insulin level and number of insulin receptors.Based on real data, some parameters such as optimum insulin level, number of insulinreceptor and minimum required energy spent were calculated by using queueing theory.Our results show an indirect correlation between insulin level and receptor. The totalenergy spent is also decreased up to optimum number of insulin receptors and then itis increased. From the results, it could be said that queuing theory predicts the optimalnumber of insulin receptors. In conclusion, the data reveals that queueing theory canbe applied to insulin level and number of insulin receptors. Estimation of insulin levelsin insulin-insulin receptor complex and number of insulin receptors obtained throughqueueing analysis may identify etiological origins of some insulin-based metabolic disorders.