Abstract
A sufficient staffing level in fire and rescue dispatch centers is crucial for saving lives. Therefore, it is important to estimate the expected workload properly. For this purpose, we analyzed whether a dispatch center can be considered as a call center. Current call center publications very often model call arrivals as a non-homogeneous Poisson process. This bases on the underlying assumption of the caller’s independent decision to call or not to call. In case of an emergency, however, there are often calls from more than one person reporting the same incident and thus, these calls are not independent. Therefore, this paper focuses on the dependency of calls in a fire and rescue dispatch center. We analyzed and evaluated several distributions in this setting. Results are illustrated using real-world data collected from a typical German dispatch center in Cottbus (“Leitstelle Lausitz”). We identified the Pólya distribution as being superior to the Poisson distribution in describing the call arrival rate and the Weibull distribution to be more suitable than the exponential distribution for interarrival times and service times. However, the commonly used distributions offer acceptable approximations. This is important for estimating a sufficient staffing level in practice using, e.g., the Erlang-C model.
Similar content being viewed by others
References
McLay L, Mayorga M (2010) Evaluating emergency medical service performance measures. Health Care Manage Sci 13(2):124–136
Schlechtriemen T, Dirks B, Lackner CK, Moecke H, Stratmann D, Krieter H, Altemeyer KH (2007) Leitstelle—Perspektiven für die zentrale Schaltstelle des Rettungsdienstes. Notf Rettungsmedizin 10(1):47–57 (in German)
Vergeiner G (1999) Bearbeitung eines Notfalleinsatzes in der Leitstelle. In: Vergeiner G (ed) Leitstellen im Rettungsdienst, Aufgaben, Organisation, Technik. Stumpf & Kossendey, Edewecht, pp 63–86 (in German)
Guenal M, Pidd M (2006) Detective work in a police force: meeting standards for call handling. In: Proceedings of the 2006 OR society simulation workshop. http://www.orsoc.org.uk/conf/simulation2006/proceedings/SW06_37PiddGunal.pdf. Accessed 20 June 2011
Hildebrand E (2006) Effizientere Notrufbearbeitung durch integrierte Regionalleitstelle. Notf Rettungsmedizin 9(5):473–477 (in German)
Law concerning rescue service in the federal state Brandenburg (BbgRettG) as at 07/14/08. GVBl.I/08 of 07/17/08(10):186–192 (in German)
Krueger U (2012) Personalbedarfsermittlung für eine Integrierte Regionalleitstelle-Dargestellt am Beispiel der Integrierten Regionalleitstelle Lausitz. Dissertation, Brandenburgische Technische Universität Cottbus, Dr. Kovac̆, Hamburg (in German)
Helber S, Stolletz R (2004) Grundlagen und Probleme der Personalbedarfsermittlung in Inbound Call Centern. Z für Betriebswirtschaft Ergänzungsheft 67(3):67–88 (in German)
Stolletz R, Helber S (2004) Performance analysis of an inbound call center with skills-based routing, a priority queuing system with two classes of impatient customers and heterogeneous agents. OR Spectr 26(3):331–352
Helber S, Stolletz R (2004) Call Center Management in der Praxis. Springer, Berlin Heidelberg (in German)
Koole G, Mandelbaum A (2002) Queuing models of call centres. Ann Oper Res 113(1–4):41–59
Hall RW (1991) Queuing methods for services and manufacturing. Prentice Hall, Englewood Cliffs NJ
Channouf N, L’Écuyer P, Ingolfsson A, Avramidis AN (2007) The application of forecasting technologies to modeling emergency medical system calls in Calgary, Alberta. Health Care Manage Sci 10(1):25–45
Matteson DS, Woodard DB, Henderson SG, McLean MW (2010) Forecasting emergency medical service call arrival rates. http://people.orie.cornell.edu/woodard/MattMcleWood.pdf. Accessed 22 February 2011
Ross S (2009) Introduction to probability statistics for engineers and scientists, 4th edn. Elsevier, Burlington San Diego, London
Tijms HC (1994) Stochastic models—an algorithmic approach. Wiley, Chichester
Mehrotra V, Grossman TA, Samuelson DA (2011) Call center management. In: Cochran JJ (ed) Wiley encyclopedia of operations research and management science. Wiley, Hoboken, New Jersey, pp 353–367
Aksin Z, Armony M, Mehrotra V (2007) The modern call center: a multi-disciplinary perspective on operations management research. Prod Oper Manag 16(6):665–688
Gans N, Koole G, Mandelbaum A (2003) Telephone call centers: tutorial, review and research prospects. Manuf Serv Oper Manag 5(2):79–141
Avramidis A, L’Écuyer P(2005) Modeling and simulation of call centers. In: Proceedings of the 2005 winter simulation conference. IEEE Press, Piscataway, NJ, pp 144–152
Koole G (2008) Introduction to the special issue on call center management. Manag Sci 54(2):237
Setzler H, Saydam C, Park S (2009) EMS call volume predictions: a comparative study. Comput Oper Res 36(6):1843–1851
Călinescu M (2009) Forecasting and capacitiy planning for ambulance services. Internsh Rep, Vrije Universiteit Amsterdam. http://www.vu.nl/Images/stageverslag-calnescutcm38-105827.pdf. Accessed 7 April 2012
Slakter M (1965) A comparison of the Pearson chi-square and Kolmogorov goodness-of-fit tests with respect to validity. J Am Stat Assoc 60(311):854–858
Kotz S, Balakrishnan N, Campbell BR, Vidakovic B, Johnson NL (2006) Encyclopedia of statistical sciences, 2nd edn. Wiley, Hoboken, New Jersey, pp 5413–6238
Johnson N, Kemp A, Kotz, S (2005) Univariate discrete distributions. 3rd edn. Wiley, Hoboken, New Jersey
Markov A (1907) Extension of the law of large numbers to dependent variables. Izv Fiz-Mat Obschch Kazan Univ Ser 2 15(4):135–256 (in Russian)
Ehrenfest P, Ehrenfest T (1907) Über zwei bekannte einwände gegen das Boltzmannsche H-Theorem. Phys Z 8(9):311–314
Eggenberger F, Pólya G (1923) Über die Statistik verketteter Vorgänge. Z Angew Math Mech 3(1):279–289
Wanner E (1951) Zur Statistik der Erdbebenschwärme. Meteorol Atmos Phys 4(1):436–448 (in German)
Marsili M, Valleriani A (1998) Self organization of interacting Pólya urns. Eur Phys J B 3(4):417–420
Eggenberger F (1924) Die wahrscheinlichkeitsansteckung. Dissertation, Technische Hochschule Zürich (in German)
Lüders R (1934) Die Statistik der seltenen Ereignisse. Biom 26(1–2):108–128 (in German)
Mahmoud H (2009) Pólya urn models. CRC Press, Boca Raton London, New York
Wei LJ (1979) The generalized Pólya’s urn design for sequential medical trials. Ann Stat 7(2):291–296
Zhang L, Hu F (2009) The Gaussian approximation for multi-color generalized Friedman’s urn model. Sci China Ser A Math 52(6):1305–1326
Hoppe F (1984) Pólya-like urns and the Ewens’ sampling formula. J Math Biol 20(1):91–94
Shah S, Kothari R, Jayadeva S, Chandra S (2009) Trail formation in ants. A generalized Pólya urn process. Swarm Intell 4(2):145–171
Xue J (2006) A Pólya urn model of conformity. Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge
Pemantle R (1990) A time-dependent version of Pólya’s urn. J Theor Probab 3(4):627–637
Ingolffson A, Akhmetshina E, Budge S, Li Y, Wu X (2002) A survey and experimental comparison of service level approximation methods for non-stationary M/M/s queuing systems. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1.2933&rep=rep1&type=pdf. Accessed 7 April 2012
http://iew3.technion.ac.il/serveng/4CallCenters/Downloads.htm (download). http://iew3.technion.ac.il/serveng/Lectures/Lecture_Markovian_Queues_Erlang_C.pdf (information). Accessed 6 April 2012
Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18(3):293–297
Marshall AW, Olkin I (2007) Life distributions. Springer, New York
Rinne H (2009) The Weibull distribution-a handbook. CRC Press, Boca Raton London, New York
Weibull W (1939) The phenomenon of rupture in solids. Ingeniörs Vetensk Ing Akad Handl 153(2):1–55
Larson RC (1972) Improving the effectiveness of New York city’s 911. In: Drake A, Keeney R (eds) Analysis of public systems. MIT Press, Cambridge, pp 151–180
Alexopolous C, Goldsman D, Fontanesi J, Kopald D, Wilson JR (2008) Modeling patient arrivals in community clinics. Omega 36(1):33–43
Lapierre SD, Goldsman D, Cochran R, DuBow J (1999) Bed allocation techniques based on census data. Socioecon Plan Sci 33(1):25–38
Côté MJ (2005) A note on “bed allocation techniques based on census data”. Socioecon Plan Sci 39(2):183–192
Acknowledgements
The authors thank the three anonymous referees for their very helpful and constructive comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Krueger, U., Schimmelpfeng, K. Characteristics of service requests and service processes of fire and rescue service dispatch centers. Health Care Manag Sci 16, 1–13 (2013). https://doi.org/10.1007/s10729-012-9207-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10729-012-9207-x