Time to Critical Condition in Emergency Services
Round 1
Reviewer 1 Report
The authors of the paper study when EMS systems reach an oversaturated state. This KPI is different than what is used in governmental policies in many countries. Hence, it also deviated from mainstream research, and this is what makes the paper potentially interesting.
There are a few major comments to make about the research.
- The authors should provide more information on why this KPI is interesting and relevant. In many countries, the response time is important, since other EMS providers can be sent in case of oversaturation. The duration of oversaturation can be very short, such that there is little impact on the response time. A better motivation for this KPI is warranted.
- In relation to the previous comment. In EMS systems, a lot of optimization is done, e.g., of proactive relocations of EMS vehicles based on the time of day. Under the KPI of response time, this leads to proactive relocations. However, under the KPI of oversaturation, this might lead to policies that do not look ahead. This further asks for justification for this KPI.
- The EMS system is modeled as an M/M/L queue. This is quite an oversimplification of the system. It is known that EMS systems behave differently at different periods of the day. Certainly, during rush hours an M/M/L system does not suffice. This model also simplifies the active relocations of EMS vehicles such that the response times will be minimized. A further justification is needed for using this model.
- The discrete-event simulation needs to be elaborated on. It is not clear to me what is being simulated, how complex of an EMS management system is modeled. What aspects of EMS management does it take into account, and which aspects are left out. Does it model an almost M/M/L model? This needs to be described better.
- The data that is used is data of an EMS system between 20.00 and 23.00 hours. Is there a specific reason for this time period? And is it a fair evaluation of the model? During the night, fewer accidents happen and the EMS system is usually less busy. For these periods, maybe an M/M/L model suffices. How does the model perform during day time?
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
This article presents a closed-form expression to calculate the mean first-passage time (MFPT) within an emergency medical services network using a birth-death process model. The article also provides a simulation framework for the MFPT. The authors did good work explaining the importance of this problem. It is a methodological paper focusing on an application domain. The application of such an approach is still a great challenge; thus, the enclosed paper could be of interest to the journal audience. I would like to offer some additional comments which could be helpful for the authors in possible revision of the manuscript.
- Figure 1 needs more context for clarification. Can the authors include an explanation/ justification of the non-linear behavior of <T> and its strong dependence on L? Why it is the case, and considering the practical setting, what does it mean? Also, what are the units of Tc, Ts, and MFPT in Figure 1?
- I would like to see the authors clarify the following questions in their Results section:
- Why did the authors choose “the real data corresponding to 2568 calls received between May 1 and October 31, 2016, late evening (20:00 to 23:00 hours)” to report? Why chose these hours? And why only these late evening hours?
- I believe there is a significant difference in the number of EMS calls at different hours of a day. In my experience, the EMS is typically much busier during the daytime. Did the author consider the variances in the number of EMS calls at different hours of the day?
- Does the service time distribution address situations where the patient does not require transit to an ED (i.e., release on the scene)?
- Following the previous comment, did the author use the historical distributions presented in Figure 3 as parameters in their simulator? If that’s the case, can the author explain why the Markov Chain Model is a valid choice for the model since the states of the system is not based on continuous time events (i.e., between May 1 23:00 and May 2 20:00, the state of the system (how many ambulances are busy/idle) is likely changed and the data do not capture the changes)?
- In Table 2, the authors compared the prediction using an exponential and three different lognormal service time distributions. Can the authors state why those three lognormal distributions were chosen (with different meanlog & sdlog)?
- Can the author elaborate on why “the analytical curves always run over the corresponding simulation” shown in Figure 5b from a modeling perspective? What factor/parameter in the model could potentially be contributing to this behavior?
- I suggest the authors carefully review the paper for grammar errors/typos in the manuscript. They should be corrected before publication. Just to point out a few:
P4 Line118: “architecture” (same in the caption of Figure 2),
P5 Line 155: “corresponding”
P6 Line 173 (the caption of Table 1): “44.1 min”
P7 Line 179: “very high values”
P11 Line 243: “which”
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
Review for the article entitled « Time to critical condition in emergency services »
This is an interesting article about the response time of emergency services. The work is mainly theoretical, with numerical simulations. The theoretical work, based on Markovian processes, is clear and well done. The approach is quite original. The only regret is that the work did not lead to the use of real data; however, the numerical simulations still give an idea of the performance of the model. For all these reasons, our opinion is to accept this article.
Comments for author File: Comments.pdf
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
I would like to commend the authors for carefully addressing the points raised in the review report.
Author Response
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Author Response File: Author Response.pdf
Reviewer 2 Report
I believe the author has addressed all my comments in the response letter. However, I didn't see the author make any changes to the revised manuscript in terms of addressing the following comments in my first review letter:
- comments 5, 6, and 8.
I suggest doing so before publication.
Author Response
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Author Response File: Author Response.pdf
