IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-3008, p-ISSN:2319-7676. Volume 10, Issue 1 Ver. I. (Jan. 2014), PP 18-22 www.iosrjournals.org www.iosrjournals.org 18 | Page Queueing Model for Medical Centers (A Case Study of Shehu Muhammad Kangiwa Medical Centre, Kaduna Polytechnic) M.O. Oladejo and M.C. Aligwo Department of Mathematics and Computer Science, Nigerian Defence Academy, Kaduna State, Nigeria Department of Mathematics/Statistics/Computer science, Kaduna Polytechnic, Kaduna State, Nigeria. Abstract: This paper examined the queueing situation in Shehu Mohammed Kangiwa Medical Center Kaduna Polytechnic. The complaints of patients on delays were corroborated by the 9minutes mean queue time and mean queue length of 3persons in the existing structure. A new multy -channel queueing model which yielded a mean queue time of 1minute and a mean queue length of 0persons was formulated. This multy-channel queueing model gave optimal results and is proposed for adoption. Key words: Medical Center, Multy-Channel Queueing Model, Patients, Queue length, Queue time. I. Introduction The rise in the population of Nigeria translates into the increase in the demand for health care services. The Federal Government of Nigeria not oblivious of the adage that “A Healthy Nation Is A Wealthy Nation” established Federal Medical Centers In every state of the federation and other medical institutions and agencies such as National Institute for Trypanosomiasis research (NITR), National Drug Law Enforcement Agency (NDLEA), the National Health Insurance Scheme (NHIS), just to mention only a few. There are also health policies in place which make provisions for services like the National Immunization program, free treatment for T.B patients etc. Government policies also encourage the private sector who augments her efforts by the establishment of private hospitals. The state governments are not left out. In fact Kaduna state government for instance has a well maintained hospital in each Local government area, with adequate supply of drugs. Pregnant women and children enjoy free health care services. All these efforts are to put a check against drug abuse, the peddling of injurious drugs, and to ensure that the citizenry is exposed to adequate health care delivery which is defined by [1] as the process by which an individual state of health is monitored, imbalances in the state and deviations from the desired state are detected and decisions are taken as to the application of available healthcare resources. 1.1 Statement of Problem The health sector, in spite of all the efforts by the federal, state governments and the private sector to provide adequate health care services to the citizenry, is still entangled with some constraints. One of these constraints is the issue of queues (delay) in our hospitals resulting in a queueing problem, [2]. This problem impedes prompt delivery of health care services, a situation which could be disastrous as human life is involved and could lead to complications or even death. 1.2 Literature Review A queue simply put is a place where customers wait before being served, [3], and they are formed when the current demand for a service exceeds the current capacity to provide the service, [4]. The problem of eliminating or reducing a queue could be very expensive as stated by [5]. But time they say is money , hence according to [6], time spent on queue is often costly therefore the dire need to solve the problem of queueing, and this in turn leads to queueing theory, According to [7], queueing theory is the development of mathematical models for analysis, forecasting and optimal decision making of systems involving queues. The idea of queueing theory can be traced back to the classical work of A.K Erlang in 1900s, however the work of D.K Kendal in 1951 formed the basis for analytical calculations and the naming convention in queues being used today [8;9] A schematic representation of the basic queueing process is given below as illustrated by [3]