Jitter Model Dispute: Mathematicians Challenge Network Engineers’ Classic Formula

When you join a video call and your colleague’s voice stutters, freezes, or arrives in awkward bursts, the culprit is usually a quantity that network engineers call jitter: the variation in the delay experienced by individual packets as they traverse the internet. For more than a decade, researchers have tried to capture this elusive metric with simple analytical formulas, because closed-form expressions allow operators to predict quality of service without running expensive simulations on live traffic. Now a quiet but pointed dispute over one such formula has erupted in the pages of a networking journal, and the exchange touches on some of the deepest conventions in queuing theory.

The controversy began when Saralees Nadarajah and A. Ba published a commentary in Frontiers in Communications and Networks in 2025, claiming that a well-known analytical model for jitter, developed by Hamza Dahmouni, André Girard, and Brunilde Sansò in 2012, contained errors in four of its central formulas. The original 2012 paper, published in the Annals of Telecommunications, had derived expressions for the average jitter experienced by a tagged stream of traffic—say, all the packets belonging to one user’s video stream—as a function of the load on a network queue. Nadarajah and Ba proposed an alternative expression that they presented as more general, and they raised three specific claims against the original work.

In a response published on 14 July 2026 in the same journal, Dahmouni, of the Institut National des Postes et Télécommunications in Rabat, together with Girard and Sansò, both of Montréal, systematically dismantled each of those claims. Their rebuttal is a masterclass in how queuing theory conventions work, and it carries a lesson for anyone who has ever tried to generalize a formula beyond the assumptions under which it was derived. The stakes are not merely academic: jitter models feed directly into the design of voice-over-IP systems, video conferencing platforms, and real-time control networks, where a few milliseconds of unmodeled delay variation can mean the difference between intelligible speech and unintelligible noise.

The first claim made by Nadarajah and Ba was that the 2012 paper suffered from confusion about which queue was actually being investigated. The rebuttal authors point out that this claim is straightforwardly inconsistent with the text of the original paper. Dahmouni and colleagues state in the abstract, in Sections 1.1 and 1.3, and again at the beginning of Section 3 that they assume Poisson traffic and exponential service times. In queuing theory, those two assumptions define precisely what is known as an M/M/1 queue in Kendall’s notation, the standard shorthand introduced by David Kendall in 1951 and codified in Leonard Kleinrock’s foundational 1975 textbook. The first M stands for the memoryless, or Markovian, arrival process; the second M for the Markovian service process; and the 1 for a single server. There is no ambiguity, the rebuttal authors argue, about what system the formulas describe.

The second and more substantive claim concerned the role of a parameter that appears in the jitter expression. Nadarajah and Ba argued that the 2012 formula is valid only under a restricted condition, and they proposed an alternative expression, which they labeled Equation 2, as a general formulation. Their proposed formula was derived from Equation 7 of the original paper under three assumptions: that the arrival process is exponential with a given parameter, that the service time is exponential with another parameter, and that the transit time—the total time a packet spends in the system—is exponential with a third parameter. Crucially, Nadarajah and Ba treated this transit-time parameter as a quantity independent of the arrival and service parameters, and they claimed that setting it equal to a particular value recovers the original 2012 result as a special case of their more general expression.

It is exactly this independence assumption that the rebuttal authors identify as the fatal flaw. In an M/M/1 queue, the transit time is well known to follow an exponential distribution whose parameter is fully determined by the arrival rate and the service rate. The mean transit time equals one over the difference between the service rate and the arrival rate, a result that appears in Kleinrock’s 1975 textbook and in W. J. Stewart’s 2009 volume on probability and queuing. In other words, the transit-time parameter is not a free variable that can be chosen at will; it is a function of the traffic parameters, and the only admissible value is the one fixed by the arrival and service rates. Substituting that admissible value into Nadarajah and Ba’s Equation 2 yields, algebraically, the original 2012 formula. The proposed generalization, the rebuttal authors conclude, collapses back into the very expression it was supposed to correct.

The third claim was perhaps the boldest: that the proposed expression could be applied to queues other than M/M/1, for instance when either the arrival or the service process is not exponential. To test this, the rebuttal authors turned to their own 2016 work on non-Poisson traffic, published by Dbira, Girard, and Sansò in the Annals of Telecommunications, and examined the case of a G/M/1 queue—a system with a general, possibly non-exponential arrival process but exponential service times. In such a queue, the transit time is still exponential, but its parameter depends on the probability that an arriving packet must wait, which itself is defined as the unique root in the interval between zero and one of an equation involving the Laplace transform of the inter-arrival distribution. That waiting probability is not an independent parameter; it depends entirely on the parameters of the inter-arrival and service-time distributions. The resulting jitter expression, the rebuttal authors show, differs fundamentally from the formula proposed by Nadarajah and Ba.

To make the point concrete, the rebuttal authors considered an arrival process following a Gamma distribution, characterized by a shape parameter and a scale parameter, combined with exponential service times. In that setting, the queue is described by three independent parameters—one for the service process and two for the arrival process—and the transit-time parameter becomes a function of all three. Nadarajah and Ba’s Equation 2, by contrast, presents the jitter as a function of three supposedly independent parameters, but once the transit-time parameter is recognized as dependent, the expression effectively contains only two independent variables while the queue it purports to describe is characterized by three. It is not clear at all, the rebuttal authors write, how such an expression could be used to compute the jitter of a G/M/1 queue. The mismatch holds for any queue in which the total number of parameters describing the arrival and service processes exceeds two.

The rebuttal authors summarize their position in five points. They state clearly that their 2012 analysis was based on exponential inter-arrival and service times, that the resulting jitter formula follows directly and is consistent with the standard definition of jitter under those assumptions, and that the interpretation of the proposed expression as a generalization appears to rely on treating the transit-time parameter as independent when, in the M/M/1 setting used to derive it, that parameter is a function of the arrival and service rates. They further note that the derivation of the proposed expression relies explicitly on the exponential form of the arrival and service processes, so further justification would be required before applying it to non-exponential processes, and that the G/M/1 example shows the proposed expression differs from known results, suggesting its use beyond the M/M/1 case may be limited.

For the broader community, the exchange is a reminder that analytical elegance and analytical validity are not the same thing. A formula that looks more general because it contains more symbols is not necessarily more general in substance; if one of those symbols is secretly determined by the others, the extra freedom is illusory. Jitter remains one of the hardest performance metrics to model in closed form, which is precisely why the Dahmouni group has spent years building a family of models, from simple M/M/1 systems with Poisson traffic to G/M/1 queues that accommodate non-Poisson arrivals. The 2026 response, edited by Koffiqa Khan of The University of the West Indies and reviewed by Santosh I. Gore, closes the loop on the specific claims but leaves the field with a durable principle: generalizations must respect the dependencies that queuing theory imposes, or they risk rediscovering, in more complicated clothing, the formulas they set out to replace.

Subject of Research: A 2026 rebuttal in Frontiers in Communications and Networks defends a classic 2012 analytical model for network jitter, showing that a proposed generalization collapses back to the original M/M/1 formula once queuing theory dependencies are respected.

Article Title: Corrections to the article ‘On the analytical model for jitter’ by Nadarajah and Ba

Article References: Dahmouni, H., Girard, A., & Sansò, B. (2026). Corrections to the article ‘On the analytical model for jitter’ by Nadarajah and Ba. Frontiers in Communications and Networks, 7, Article 1803255. https://doi.org/10.3389/frcmn.2026.1803255

Image Credits: AI Generated

DOI: 10.3389/frcmn.2026.1803255

Keywords: jitter, queuing theory, M/M/1 queue, packet delay variation, communication networks, quality of service, VoIP, analytical modeling, Corrections, article, analytical, model