In this paper we examined effects of lipid induced insulin resistance on insulin stimulation of endoplasmic reticulum (ER) stress. mRNAs of several ER stress markers were determined in fat biopsies obtained before and after 8-h hyperglycemic hyperinsulinemic clamping in 13 normal subjects and in 6 chronically insulin resistant patients with type 2 diabetes mellitus (T2DM). In normal subjects, hyperglycemia hyperinsulinemia increased after/before mRNA ratios of several ER stress markers. Lipid infusion was associated with inhibition of the PI3K insulin signaling pathway and with a decrease of hyperinsulinemia induced ER stress responses. In chronically insulin resistant patients with T2DM, hyperglycemic hyperinsulinemia did not increase ER stress response marker mRNAs. Single server queue with random accumulation level and analysis of the continuous time parameter process is used to find the effects of lipid induced insulin resistance on UPR mRNA with the help of normal distribution.