Introduction
Given the importance of jitter to the quality of service in real-time applications and the lack of simple analytical models that accurately capture this performance metric, we have developed several analytical models since 2009 to describe jitter behavior under various scenarios. These models range from simple queuing systems, such as M/M/1 with Poisson traffic (), to more complex systems, such as G/M/1 queues (), which account for non-Poisson traffic.
Jitter is a measure of the variation of a packet’s transfer delay and is defined by the IETF () as follows. Let represent the delay experienced by packet going through a queue. The average jitter is then given by the expected value of the absolute jitter:
In Section 3 of our paper,
, we developed analytical formulas for the jitter of a tagged traffic stream, e.g., all the packets of a particular movie being watched by a user, as a function of its load. The authors of
claim that our formulas (9–12) are incorrect and propose an alternative expression, which they present as more general. They make the following claims.
Claim 1: There is some confusion in regarding the queue being investigated.
Claim 2: Our formula , developed in , is valid only when . They propose Equation 2 as a general formulation.
Claim 3: Their expression (Equation 2) is a more general formula for the jitter as it can be applied to queues other than M/M/1.
We now explain why these claims appear inconsistent with established results.
On claim 1: confusion regarding our gueue model
In , we specifically state that we consider Poisson traffic and exponential service times in the abstract, in Sections 1.1 and 1.3, and at the beginning of Section 3. In queuing theory, this defines an M/M/1 queue using Kendall’s notation (). Thus, the queueing model is specified as an M/M/1 queue under the stated assumptions of Poisson arrivals and exponential service times.
On claim 2: the role of
Their proposed extended jitter formula
The authors of propose the following Formula 2 for computing the jitter
This is derived from
Equation 7of
under the following assumptions:
the arrival process is exponential with parameter ;
the service time is exponential with parameter ; and
the transit time is exponential with parameter ;
In Equation 2, is viewed as a parameter independent of and . The authors further indicate that their formula is more general than ours since our result is a special case of Equation 2, which can be derived as follows. Setting , the two terms in the denominator becomeSubstituting them in Equation 2, we obtain
Our response:
First, recall the fundamental assumptions of an M/M/1 queue and the relationship between , , and , as can be found in and .
An M/M/1 queue is defined by exponential inter-arrival times and also exponential service times .where is the arrival rate and is the service rate, and the usual stability condition holds.
Under these assumptions, it is well known (; ) that the system (or transit) time follows an exponential distribution with parameter and that the mean transit time is given by
In other words, for the M/M/1 queue, the parameter is fully determined by the traffic parameters and and, therefore, cannot be considered independent: the only admissible value is . Substituting Equation 4 into Equation 2 yields , which is our result.
On claim 3: generalization to other queues
Even though the derivation of Equation 2 relies on the M/M/1 assumption, the authors claim that it can be applied to other types of queues, for instance, when either the arrival or the service process is not exponential. This has been studied in , and we take the simple case of a general arrival and exponential service, a G/M/1 queue, to show how the jitter can be computed for non-Poisson queues.
We know from that the transit time of a G/M/1 queue follows an exponential distributionwhere is the transit rate and is the probability of waiting, given by the unique root in the interval (0, 1) ofwhere , the Laplace transform of the inter-arrival distribution , is given by
A very important point is that is not an independent parameter but instead depends entirely on the parameters of the inter-arrival and service-time distributions. From this, we can show thatwhich is very different from Equation 2.
Consider now the case where the inter-arrival distribution is a Gamma, , with shape and scale . We haveandwhich can be replaced in Equation 9. This means that is a function of three independent parameters: for the service time and and for the arrival times. In that expression, is also a function of the same parameters from Equations 4–8, 10, 11.
In , on the other hand, Equation 2 is presented as a function of three independent parameters , , and . We know, however, that is not an independent variable, which leaves an equation with two independent variables and , while the queue is characterized by three independent variables , , and .
For this reason, it is not clear at all how Equation 2 could be used to compute the jitter of a G/M/1 queue. This holds for any queue in which the total number of parameters describing the arrival and service processes is greater than 2.
Conclusion
To summarize,
We have clearly stated that our analysis is based on exponential inter-arrival and service times, i.e., the M/M/1 queue model.
Within this framework, the expression , follows directly and is consistent with the definition of jitter under these assumptions.
The interpretation of expression (Equation 2) as a generalization for any appears to rely on treating as an independent parameter. However, in the M/M/1 setting used to derive (Equation 2), is a function of and , which limits the generalization of (Equation 2) to other values.
The derivation of (Equation 2) relies explicitly on the exponential form of the arrival and service processes. Further justification would be required before applying this expression to non-exponential arrival or service processes.
The example of the G/M/1 shows that expression (Equation 2) differs from the known results , which further suggests that its use beyond the M/M/1 case may be limited.
Statements
Author contributions
HD: Writing – original draft, Writing – review and editing. AG: Writing – original draft, Writing – review and editing. BS: Writing – original draft, Writing – review and editing.
Funding
The author(s) declared that financial support was not received for this work and/or its publication.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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References
1
DahmouniH.GirardA.SansòB. (2012). An analytical model for jitter in IP networks. Ann. Telecommun.67, 81–90. 10.1007/s12243-011-0254-y
2
DbiraH.GirardA.SansòB. (2016). Calculation of packet jitter for non-Poisson traffic. Ann. Telecommun.71, 223–237. 10.1007/s12243-016-0492-0
3
DemichelisC.ChimentoP. (2002). RFC 3393: IP packet delay variation metric for IP performance metrics (IPPM). IETF.
4
KleinrockL. (1975). Queuing Systems. Wiley.
5
NadarajahS.BaA. (2025). On the analytical model for jitter. Front. Commun. Netw.6, 1602095. 10.3389/frcmn.2025.1602095
6
StewartW. J. (2009). Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press.
Summary
Keywords
communication networks, jitter, M/M/1 queue, packet delay variation, queuing
Citation
Dahmouni H, Girard A and Sansò B (2026) Corrections to the article ‘On the analytical model for jitter’ by Nadarajah and Ba. Front. Commun. Netw. 7:1803255. doi: 10.3389/frcmn.2026.1803255
Received
03 February 2026
Revised
04 June 2026
Accepted
09 June 2026
Published
14 July 2026
Volume
7 - 2026
Edited by
Koffka Khan, The University of the West Indies St. Augustine, Trinidad and Tobago
Reviewed by
Santosh I. Gore, Sai Info Solution, India
Updates
Copyright
© 2026 Dahmouni, Girard and Sansò.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: André Girard, andre.girard@gerad.ca
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.