Mathematical analysis of single queue multi server and multi queue multi server queuing models: comparison study

Prasad, Vijay Shankar; V.H, Badshah; Koka, Tariq Ahmad

doi:10.14419/gjma.v3i3.4689

Cited by 9 publications

(5 citation statements)

References 4 publications

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“…Thus, the total no. of patients in the system is defined as s ∈ {0,1,...,c−1,c}, so the associated birth-death process comprises a finite number of states (Prasad, and Koka, 2015).…”

Section: Distributionsmentioning

confidence: 99%

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simulation-based approach for minimizing waiting time in AIIMS, Delhi using Queuing model

Sharma

2022

ijhs

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The government hospitals in India influenced by multiple factors causing longer waiting time of patients in comparison to private hospitals, which worsen the threat to healthcare facilities. The optimization of available resources considering the arrival rate of patients and the availability of facilities for the minimization of queuing is the utmost requirement. The current study has been carried out within the outpatient's department to minimize queue length of one of the largest and busiest hospital, AIIMS in Delhi, represent a struggling health care delivery system with high waiting times of patients. The primary queuing data was collected for total samples of 1200 patients during the four-week study period (1st July to 30th July 2020), (Monday-Friday) and working hours of general OPD (08:30 am to 01:00 pm). The detailed queuing secondary data was collected from AIIMS for three years (1st January 2015 to 31st July 2017). Data has been analyzed by queuing models, M/M/1: Poisson-exponential, single server model-infinite population and up to M/M/8: Poisson-exponential, multiple server model-infinite populations.

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“…Thus, the total no. of patients in the system is defined as s ∈ {0,1,...,c−1,c}, so the associated birth-death process comprises a finite number of states (Prasad, and Koka, 2015).…”

Section: Distributionsmentioning

confidence: 99%

“…Service Time: Difference between the time a patient entered until when he/she exited the system/mean time in the system Length of Queue: The length of the queue at a particular point in time (Prasad, V.H and Koka, 2015) 5…”

Section: Waiting Timementioning

confidence: 99%

simulation-based approach for minimizing waiting time in AIIMS, Delhi using Queuing model

Sharma

2022

ijhs

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“…Prasad et al [9] presented a mathematical modelling and a comparison study of two queueing models: single-queue multi-server and multi-queue multiserver. They have proven in the study that the mean total cost of single-queue multi-server is less, for their model, than multi-queue multi-server.…”

Section: Literature Reviewmentioning

confidence: 99%

Queueing model analysis of shopping malls in COVID-19 pandemic era: a case study

Al-Kadhimi¹,

Abdulkadhim²,

Ali³

2021

IJATEE

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Queueing forms a daily routine of our lives wherever there are limitations in resources with competition. The ongoing Coronavirus Disease of 2019 (COVID-19) pandemic undeniably has its impacts on people's daily life. That in turn affected the number of customers who used to go outside for different outdoor activities. In this paper, a shopping mall is considered as a case study to propose an appropriate queueing model within these current pandemic circumstances. The proposed model consists of an open network with 10 nodes represent different real-existing serving stations. The queueing model is first analysed to check its stability that is evident analytically on the long run. The performance of the proposed network model is investigated using different measures. Based on recorded arrival and service rates, the mathematical derivations show that the traffic intensity of the system is still below 1, hence ensures stability. Also, the average number of customers in the network is 16.76 customers with only 2.66 customers awaiting in queues.Furthermore, the mean time a customer spends in the queue is only 0.16 min from a total spend on the network about 1.006 min. This indicates that the majority of time customers spend is in service with a very short waiting time due to current COVID-19 pandemic consequences, and the waiting time and queue lengths will undoubtedly increase once normal social life resumes.

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“…This paper the queue sorting is performed by IoT devices through the optimized study of various types of queuing methods, such as single server queue, multi-server parallel queue, and On Demand queue [5]. The multi server multi queue (Isolated queue) initiated and derived by Vijay Prasad and Badshah [6,7] and also studied M/M/s queuing model for decision making coauthored with Pradeep Porwal [8]. In supermarkets single queue is better than multiple queue is investigated by Xia and Zhang [9].…”

Section: Literature Reviewmentioning

confidence: 99%

Mathematical modeling in comparative relation of single queue multi server and multi queue multi server queuing models

Mariyappan¹,

Alexander²,

Anbalagan³

2020

Malaya J. Mat.

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Customers waiting to get service from server are portrayed by queue and also called waiting line. Unsatisfied customer due to lengthy queue can be potential loss to any service organization. In single queue single server, the above mentioned potential loss is higher. So, we deal with single queue multi server. This motivates us for the study among single queue multi server and multi queue multi server which one is best according to the expected total cost. In this paper, we revealed the total cost with assumption of service cost and waiting cost is better in single queue multiple server than multiple queue multiple server in supermarket checkouts counters.

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Mathematical analysis of single queue multi server and multi queue multi server queuing models: comparison study

Cited by 9 publications

References 4 publications

simulation-based approach for minimizing waiting time in AIIMS, Delhi using Queuing model

simulation-based approach for minimizing waiting time in AIIMS, Delhi using Queuing model

Queueing model analysis of shopping malls in COVID-19 pandemic era: a case study

Mathematical modeling in comparative relation of single queue multi server and multi queue multi server queuing models

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