Two important resources in a call center are the number of staff and the number of trunk lines required. In this paper, we focus on the decision of the number of trunk lines that a call center should have. The current practice is to use the Erlang B or the M/M/s/0 queueing model which assumes Poisson arrivals, exponential service times, s servers and no places in queue, i.e. no customers can wait. In this paper, we improve on the state of practice in determining the required number of trunk lines, by including two realistic features present in call centers. The first realistic feature is to consider nonstationarity of arrivals. The second feature is to consider the lognormal service time distribution instead of the exponential distribution. There is extensive empirical evidence for both features. In order to carry out our computations we use the results of a paper by Massey and Whitt, Operations Research, 44(6), 1996. We have two main findings. Firstly, we find numerically that in our nonstationary Erlang loss model, Mt/G/s/0, an insensitivity result holds. The blocking probability of arrivals at the call center depends only on the mean of the lognormal service time distribution and not on its variance. Our second finding is that current practice is quite robust. In particular, we find the number of trunk lines required using a stationary Poisson approximation. This approximation assumes stationary Poisson arrivals with an appropriately chosen arrival rate and exponential service times. The approximation does quite well in predicting the number of trunk lines required.
| Published in | American Journal of Operations Management and Information Systems (Volume 4, Issue 3) |
| DOI | 10.11648/j.ajomis.20190403.11 |
| Page(s) | 71-79 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Queueing, OR in Service Industries, Call Centers, Nonstationary Arrivals, Lognormal Distribution
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APA Style
Siddharth Mahajan. (2019). Determining Trunk Lines in Call Centers with Nonstationary Arrivals and Lognormal Service Times. American Journal of Operations Management and Information Systems, 4(3), 71-79. https://doi.org/10.11648/j.ajomis.20190403.11
ACS Style
Siddharth Mahajan. Determining Trunk Lines in Call Centers with Nonstationary Arrivals and Lognormal Service Times. Am. J. Oper. Manag. Inf. Syst. 2019, 4(3), 71-79. doi: 10.11648/j.ajomis.20190403.11
AMA Style
Siddharth Mahajan. Determining Trunk Lines in Call Centers with Nonstationary Arrivals and Lognormal Service Times. Am J Oper Manag Inf Syst. 2019;4(3):71-79. doi: 10.11648/j.ajomis.20190403.11
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Download@article{10.11648/j.ajomis.20190403.11,
author = {Siddharth Mahajan},
title = {Determining Trunk Lines in Call Centers with Nonstationary Arrivals and Lognormal Service Times},
journal = {American Journal of Operations Management and Information Systems},
volume = {4},
number = {3},
pages = {71-79},
doi = {10.11648/j.ajomis.20190403.11},
url = {https://doi.org/10.11648/j.ajomis.20190403.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajomis.20190403.11},
abstract = {Two important resources in a call center are the number of staff and the number of trunk lines required. In this paper, we focus on the decision of the number of trunk lines that a call center should have. The current practice is to use the Erlang B or the M/M/s/0 queueing model which assumes Poisson arrivals, exponential service times, s servers and no places in queue, i.e. no customers can wait. In this paper, we improve on the state of practice in determining the required number of trunk lines, by including two realistic features present in call centers. The first realistic feature is to consider nonstationarity of arrivals. The second feature is to consider the lognormal service time distribution instead of the exponential distribution. There is extensive empirical evidence for both features. In order to carry out our computations we use the results of a paper by Massey and Whitt, Operations Research, 44(6), 1996. We have two main findings. Firstly, we find numerically that in our nonstationary Erlang loss model, Mt/G/s/0, an insensitivity result holds. The blocking probability of arrivals at the call center depends only on the mean of the lognormal service time distribution and not on its variance. Our second finding is that current practice is quite robust. In particular, we find the number of trunk lines required using a stationary Poisson approximation. This approximation assumes stationary Poisson arrivals with an appropriately chosen arrival rate and exponential service times. The approximation does quite well in predicting the number of trunk lines required.},
year = {2019}
}
TY - JOUR T1 - Determining Trunk Lines in Call Centers with Nonstationary Arrivals and Lognormal Service Times AU - Siddharth Mahajan Y1 - 2019/08/05 PY - 2019 N1 - https://doi.org/10.11648/j.ajomis.20190403.11 DO - 10.11648/j.ajomis.20190403.11 T2 - American Journal of Operations Management and Information Systems JF - American Journal of Operations Management and Information Systems JO - American Journal of Operations Management and Information Systems SP - 71 EP - 79 PB - Science Publishing Group SN - 2578-8310 UR - https://doi.org/10.11648/j.ajomis.20190403.11 AB - Two important resources in a call center are the number of staff and the number of trunk lines required. In this paper, we focus on the decision of the number of trunk lines that a call center should have. The current practice is to use the Erlang B or the M/M/s/0 queueing model which assumes Poisson arrivals, exponential service times, s servers and no places in queue, i.e. no customers can wait. In this paper, we improve on the state of practice in determining the required number of trunk lines, by including two realistic features present in call centers. The first realistic feature is to consider nonstationarity of arrivals. The second feature is to consider the lognormal service time distribution instead of the exponential distribution. There is extensive empirical evidence for both features. In order to carry out our computations we use the results of a paper by Massey and Whitt, Operations Research, 44(6), 1996. We have two main findings. Firstly, we find numerically that in our nonstationary Erlang loss model, Mt/G/s/0, an insensitivity result holds. The blocking probability of arrivals at the call center depends only on the mean of the lognormal service time distribution and not on its variance. Our second finding is that current practice is quite robust. In particular, we find the number of trunk lines required using a stationary Poisson approximation. This approximation assumes stationary Poisson arrivals with an appropriately chosen arrival rate and exponential service times. The approximation does quite well in predicting the number of trunk lines required. VL - 4 IS - 3 ER -
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