Minimize Aggregate Measure of Waiting Times and Queue Lengths in M/G/1 Queue
Roweda M.A. Mahmuod1, Rahela Rahim2
1Roweda M.A. Mahmuod, School of Quantitative Sciences, College of Arts and Sciences, University Utara Malaysia, Sintok, Kedah, Malaysia.
2Rahela Rahim, School of Quantitative Sciences, College of Arts and Sciences, University Utara Malaysia, Sintok, Kedah, Malaysia.
Manuscript received on 01 February 2019 | Revised Manuscript received on 07 February 2019 | Manuscript Published on 13 February 2019 | PP: 177-180 | Volume-8 Issue- 4S February 2019 | Retrieval Number: DS2856028419/2019©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The classic optimization techniques are helpful to find the optimum resolution or free maxima or minima of continuous and differentiable functions. The target of this study is to develop a replacement formula to solve the pedestrian congestion problem based on queuing theory and optimization that will lead to an efficient algorithm for pedestrian flow in optimizing allocation of pedestrian and service capacity subject to limited buffer space by show a mathematical model that minimizes an aggregate measure of waiting times and queue lengaths for a group of arrivals by using Lagrange multiplayer. Ls (expected variety of consumers within the ith system, Ws (expected time employment spends within the ith system), Lq(expected variety of consumers within the queue in the ith system) ,Wq(Expected time employment spends in the queue in the ith system) decreased compared with the naïve value of λi. A queuing model calculator used to calculate the optimal values.
Keywords: Queuing Network, Optimization, M/G/1 queue.
Scope of the Article: Cryptography and Applied Mathematics