This textbook comprises with outcomes of post-doctoral D.Sc. Thesis of Prof. (Dr.) Vishwa Nath Maurya; an Indian Academician and presently working at Science & Technology, University of Fiji. As such, the present textbook; a version of D.Sc. Thesis is utmost useful for doctoral and post-doctoral research scholars of all Indian and Foreign Universities in the field of Applied Mathematics, Statistics, Queueing Networks, Computer Science, Reliability & Industrial Engineering. However, as per design and curriculum of the textbook, it is useful for post-graduate students also. Outcomes of the text are supported by numerical illustrations, tables & graphs. Relevant interesting theorems are developed which are significant from application point of view in various public and private sectors such as in Railways System, Hospitals and Health Care Services, Business Organizations & Machine Repair System & other Service Centers. The textbook is entirely based on over 20 scientific research papers at post-doctoral level; published in various Indian & Foreign leading International journals of USA, Malaysia & Nigeria. It is highly expected from readers to explore present research work in future.