M/M/1 Queue with N-Policy Two-Phase, Server Start-Up, Time-Out and Breakdowns
A.Ankamma Rao1, V.N. Rama Devi2, K.Chandan3
1A.AnkammaRao*, Research scholar, Department of Statistics, Acharya Nagarjuna University, Guntur, AP, India.
2V.N.Rama Devi, Associate Professor, Department of Mathematics, GRIET, Hyderabad, Telangana, India.
3K.Chandan, Professor, Department of Statistics, Acharya Nagarjuna University, Guntur, AP, India.
Manuscript received on November 19, 2019. | Revised Manuscript received on November 29 2019. | Manuscript published on 30 November, 2019. | PP: 9165-9171 | Volume-8 Issue-4, November 2019. | Retrieval Number: D9044118419/2019©BEIESP | DOI: 10.35940/ijrte.D9044.118419
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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: This paper analyzes M/M/1 vacation two-phase queueing model with server Start-up, Time-out and Breakdowns. Customers arrivals are assumed as Poisson process and be given batch mode in the first phase followed by individual models second phase. Arrivals during batch service are allowed to enter the batch without Gating. After providing the second phase of service to all customers individually, server returns to first phase to serve the existing customers followed by individual service. If no one presents, then server waits for a fixed time ‘C’ is called server Time-out. If units arrived during this fixed time, then the server starts the cycle again by providing them batch service followed by individual service, otherwise after expiration of fixed time he takes a vacation. The server comes back from vacation, after N-customers are accumulated. The server passes a random period as pre-service procedure after coming back from vacation. During individual service the server is susceptible to random failures. Various performance measures are evaluated in steady state. Cost function is established to define the threshold and sensitivity analysis is also presented through numerical examples.
Keywords: Vacation, Two-phase, Pre-service, Time-Out and Server Breakdown.
Scope of the Article: Pervasive Computing.