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Strict-Priority Packet Delay in Switches with Transmit-Ring Buffering
arXiv:2606.09619v1 [cs.NI] 8 Jun 2026
Yash Deshpande, Quirin Vogel, Wolfgang Kellerer.
Abstract—Strict Priority (SP) scheduling is widely used at switch egress to provide low latency service to high-priority (HP) traffic. Existing deterministic and stochastic latency models typically account for scheduler behavior and packet transmission, but omit a common switch implementation detail: the transmit ring (TXR) between the scheduler and the physical port. Because the switch must prepare the next packet before the current transmission completes, packets already placed in the TXR can further delay HP packets. This changes both the worst-case delay and the per-hop delay distribution of the HP packets. This paper identifies this modeling gap, extends standard SP latency models to include the TXR, and validates the revised model through measurements on multiple switches. This paper also provides a measurement method for estimating the TXR size, a parameter that is often not reported in switch datasheets. The resulting model provides a closer representation of switch behavior for systems that use SP scheduling and require either delay bounds or delay distributions. Index Terms—Packet delay, deterministic networking, network calculus, latency measurement.
I. I NTRODUCTION Packet scheduling at switch egress is a standard mechanism for providing different quality-of-service classes to different flows. In industrial networks, safety-critical systems, and deterministic networking deployments, these scheduling mechanisms are often used to support latency guarantees for highpriority (HP) traffic. Analytical methods such as deterministic network calculus model the scheduler and derive per-hop delay bounds from traffic and service assumptions [1], [2]. Strict Priority (SP) scheduling is a common choice for lowlatency HP traffic. It is available in many commercial off-theshelf switches, including devices used in industrial, enterprise and data-center networks across. This availability has made SP scheduling a frequent building block in deterministic networking studies, including joint scheduling and routing formulations on commodity switches [3]–[5]. In these models, HP traffic is assumed to receive service before low-priority (LP) traffic whenever both are waiting at the scheduler. Beyond worst-case bounds, stochastic network calculus and measurement-based analyses use per-hop delay distributions to estimate the probability of deadline violations [2]. Delay distributions are also useful for other timing-sensitive functions. For example, they can affect estimates of clocksynchronization error when packet delay variation contributes to delay assymetry [6]. Accurate per-hop delay models are therefore needed not only for strict guarantees, but also for probabilistic and statistical performance analysis. This paper shows that standard SP latency models miss an implementation constraint that is present in most switches. To Yash Deshpande and Wolfgang Kellerer are with the Chair of Communication Networks at the Technical University of Munich. Quirin Vogel is with the Department of Statistics, University of Klagenfurt, Austria.
Fig. 1. Egress architecture showing the post-scheduler TXR.
avoid idle time and packet-selection overhead at line rate, a switch may load one or more packets into a transmit ring (TXR) after the scheduler and before the physical egress port [7]. This architecture is illustrated in Fig. 1. Once a packet is placed in this TXR, it can no longer be preempted by a later HP arrival. As a result, an HP packet can be delayed by LP packets that have already passed the scheduler. This effect is not captured by models that treat the scheduler as the last queueing point before transmission. The TXR changes both deterministic and stochastic latency analysis. In the worst case, the HP packet may wait behind multiple LP packets already present in the TXR. In the stochastic case, the delay distribution depends on the occupancy of the TXR and on the interfering LP traffic. The relevant TXR size is usually not exposed as an operator setting, and it is often absent from switch datasheets. Reducing the ring size, when possible, may also increase CPU load or reduce forwarding efficiency. This work makes two contributions: (1) We identify the TXR as a source of discrepancy between standard SP latency models and observed HP packet delay. Measurements across different network switches show that this discrepancy exists in almost all the devices. (2) We extend the standard perhop SP delay model to include the TXR size, for both worstcase latency and delay distributions. We validate the model using measurements and provide a measurement method for estimating the TXR size. The revised model can be used in latency analyses that require packet delay bounds or delay distributions for SP-based networks. II. BACKGROUND Ethernet switches classify packets before enqueueing them at an egress port. The classification can use link-layer markings, such as the Priority Code Point (PCP) field in IEEE 802.1Q VLAN tags, or network-layer markings, such as the Differentiated Services Code Point (DSCP) field used by Differentiated Services (DiffServ). The selected marking is mapped to one of the egress queues configured on the port. Commercial off-the-shelf switches commonly expose four or eight such priority queues per egress port. Other common egress schedulers include round robin, weighted round robin, and interleaved weighted round robin. Among these schedulers, SP provides the lowest guaranteed latency to HP packets.
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1 SNC Empirical DNC
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Delay (µs) Fig. 2. Empirical HP latency CDF versus the CDF predicted by a standard SNC model. The measured latencies show a different distirbution and violate the DNC bound.
Under SP queueing, the scheduler always selects a packet from the highest non-empty priority queue. Therefore, an HP packet is dequeued before any LP packet that is still waiting at the scheduler. This rule is the basis for standard deterministic network calculus (DNC) models of SP scheduling, where LP traffic can affect an HP packet only through the packet already in transmission when the HP packet arrives [1]. stochastic network calculus (SNC) models use related assumptions to derive a delay-violation probability or a delay distribution [2]. Fig. 2 illustrates the discrepancy studied in this paper. In this example, three LP flows send 1500-byte packets at 200 Mbps each on a 1 Gbps link, while one HP probe packet arrives at a random time once per second. We measure 27,000 HP packet latencies and compare the empirical distribution with the distribution predicted by standard network-calculus models. Under the standard DNC model, the worst-case queueing delay is the non-preemptive blocking time of one packet, dDNC = L/C = 1500 · 8/109 = 12 µs, where L is the q packet size and C is the link capacity. The corresponding total delay is the maximum processing delay, dmax proc = 5.32µs, value is measured over 10,000 added to this value. The dmax proc HP probe samples without LP flows. Alternatively, if available, one can refer the RFC2544 [8] test results of the switch. The SNC model predicts that the total-delay probability density function (PDF) is a mixture distribution: with probability 0.4 it is Gaussian, representing probes that are not queued, and with probability 0.6 it is the sum of a Gaussian term and a ]. The two distributions uniform random variable on [0, dDNC q differ in the queuing regime. The same discrepancy affects worst-case analysis. If the traditional DNC model is used as the target latency, the predicted bound can be lower than the measured latency for 22% of the probes in this experiment. This means that the model can underestimate the latency target even when the scheduler is configured as expected. The DNC bounds are supposed to be strict, and therefore a violation to it untenable for certain applications. The same effect was observed in prior work, but it was treated as a priority-queue overhead [9]. That study measured line-rate saturated LP queues and did not analyze the full latency distribution. It also did not identify why the overhead differs across switches. The cause is the TXR located after the scheduler and before the physical egress port as shown in Fig. 1. Before the currently transmitted packet completes, the scheduler can already dequeue the next packet from the priority queues and place it in the TXR. This allows the switch to prepare the next transmission in advance and avoids egress-port idle time. Once an LP packet has entered this queue, a later HP packet cannot
overtake it, even though SP scheduling would have selected the HP packet if both packets were still in the priority queues. The TXR capacity is usually a number of packets, and this value determines how many already-dequeued packets can block a later HP packet. Over a variety of switches measured in Sec. V-A, we determined that the TXR size is between 2-4 packets. Only for 1G Time-Sensitive Networking (TSN) switches capable of IEEE 802.1Qbu frame preemption, TXR size was 1 packet. In the next section, we formulate the problem, introduce the notation, and give the main results for the packet-delay bound and delay distribution as functions of the LP traffic characteristics. The following section describes the measurement setup and validates the proposed model. To the best of our knowledge, this is the first work to provide both a worst-case and a probabilistic queue-delay model for SP scheduling that explicitly includes the post-scheduler TXR. III. S YSTEM M ODEL We consider a single egress port configured with SP scheduling. From the perspective of HP packets, all queues with lower priority than the HP queue can be abstracted into a single aggregate LP queue [1], [10]. This abstraction is sufficient because an HP packet is affected only by lowerpriority packets that are either already in service or already placed in the post-scheduler TXR. We assume that at most one HP packet is present in the system at any time. The HP packet arrives at a random time and serves as a probe for the instantaneous delay caused by the LP traffic and the TXR. If this assumption is relaxed, an arrival process for the HP flow(s) must additionally be specified, since HP packets may then queue behind other HP packets. Let C denote the link capacity. We consider N enumerated LP flows indexed by f ∈ 1, . . . , N . Each LP flow f is characterized by a fixed packet size Lf in bytes and a rate ρf . The rate ρf is expressed as a fraction of the link capacity C and therefore satisfies 0 ≤ ρf ≤ 1. The TXR has a capacity of B packets. We assume that the priority queues before the scheduler have infinite capacity. Buffer overflow is excluded PN by requiring that the aggregate LP load ρ satisfies, ρ = f =1 ρf ≤ 1. This condition ensures that the aggregate LP input rate is sustainable by the egress link in the long term. IV. A NALYSIS A. Without TXR 1) Stochastic: Let DHP be a random variable that denotes the delay experienced by an HP packet. We model this delay as the sum of two independent components, DHP = D0 + DLP , where D0 represents the baseline system delay and DLP represents the additional delay caused by LP traffic already occupying the server or the TXR. The baseline delay D0 captures processing, propagation, and other stochastic system effects unrelated to queue occupancy. It is modeled as a Gaussian random variable D0 ∼ N (µ, σ 2 ), with mean µ and variance σ 2 . The additional delay component DLP is modeled as a mixed random variable determined by the instantaneous state of the LP traffic at the arrival instant of the HP packet. Under SP
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scheduling with TXR, an arriving HP packet can only be blocked by a LP packet that is already in transmission. Due to the random arrival instant of the HP packet, the remaining service time of a blocking packet is uniformly distributed over the serialization interval of that packet. For a LP flow f , the Lf ·8 serialization delay is Tf = C . The blocking delay caused by flow f is therefore modeled as a uniformly distributed random variable from 0 to the serialization dely, Uf ∼ U (0, Tf ), because the HP packet can arrive at anytime during the transmission of the LP packet. With probability 1 − ρ, no LP packet is encountered and therefore no additional blocking delay occurs. With probability ρf , the HP packet is blocked by a packet belonging to flow f . Consequently, the random variable DLP follows the mixed distribution N X
DLP ∼ (1 − ρ) δ(x) +
ρf U(0, Tf ),
f =1
where δ(x) denotes the Dirac delta distribution representing zero blocking delay. The overall delay distribution of the HP packet is therefore obtained as the convolution of the Gaussian baseline delay with the mixed blocking-delay distribution, fDHP (x) = (1 − ρ)fG (x) +
N X
ρf fG ∗ fUf (x),
f =1
where fG (x) denotes the Gaussian probability density function and ∗ denotes convolution. The convolution can be explicitly solved and simplified as fDHP (x) = (1−ρ)fG (x)+
N X f =1
ρf
B. With TXR 1) Stochastic: In the previous model, only a single LP packet could block the arriving HP packet. However, when a TXR of capacity B packets is present, multiple LP packets may already occupy the transmission pipeline ahead of the arriving HP packet. We now define the stochastic TXR model by explicitly accounting for the occupancy contribution of each LP flow. Let K ∈ {0, 1, . . . , B} denote the random number of LP packets located ahead of the arriving HP packet, including packets currently in transmission and packets buffered inside the TXR. The occupancy distribution of K depends on the interaction between the LP flows, including their arrival characteristics and batching (burst) behavior. In this work, we do not explicitly model these arrival processes. Instead, the aggregate occupancy behavior is represented PBby the probability mass function pk = Pr(K = k) with k=1 pk = ρ, i.e th total steady state probability that a packet is blocked is the aggregate rate of all the flows. Conditioned on the event K = k, there exist multiple possible compositions of the k blocking packets across the N LP flows. We need to be careful and distinguish the serialization delay of a packet being served and the packets already loaded. Denote the flow former by g. Let furthermore n(k) = (n1 , . . .P , nN ) denote one such composition of loaded packets, N where f =1 nf = k − 1, and nf represents the number of packets belonging to flow f . Each valid composition is associated with conditional probabilities, χf = Pr(g = f | K ≥ 1) , (k,f ) as well as πn = Pr n(k) | K = k, g = f , satisfying
FG (x) − FG (x − Tf ) , (1) Tf
where FG is the associated Gaussian cummulative distribtuion function. This model captures the key behavior of SP scheduling without a post-scheduler TXR: in the absence of LP blocking, the delay follows the baseline Gaussian behavior, whereas the presence of a LP packet introduces an additional uniformly distributed serialization delay whose magnitude depends on the corresponding packet size. 2) Deterministic: DNC provides a deterministic upper bound on the HP packet delay. In this case, the stochastic baseline delay component is replaced by its maximum observed value denoted by dmax proc .One can also use a percentile based cutoff on a gaussian with µ, σ 2 to obtain dmax proc . Under SP scheduling, the worst-case blocking occurs when the arriving HP packet encounters the largest possible LP packet just about to start a transmission. Let F ∈ arg maxf ∈{1,...,N } Lf denote an LP flow with maximum packet size. The resulting deterministic upper bound on the HP packet delay is therefore given by max dDNC HP = dproc + TF .
(2)
This bound corresponds to the classical non-preemptive SP worst-case analysis, where the HP packet may be blocked by at most one LP packet from flow F .
N X
χf = 1
and
f =1
X
πn(k,f ) = 1,
n(k)
where the summation is taken over all valid compositions of k packets across the N flows. Conditioned on a specific composition n(k) , the total LP blocking delay is therefore given by (k,n)
DLP
= U(0, Tg ) +
nf N X X f =1 i=1
Tf,i = U(0, Tg ) +
N X
nf Tf .
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(3) Another phenomenon that is not modelled in typical DNC and SNC so far is the arbitration latency (AL) [11]. Modern switches often implement priority queues using shared internal buffers or virtual queues. When the SP scheduler selects one packet from these queues, the selection step can introduce an overhead in the form of AL. We also measured this overhead in our tests and the following phenmonena was observed: instead of continous translated uniform k-dependent blocks (see (3)), a gap between the uniform components of the law of DHP appear. Mathematically, this can by expressed by introducing a parameter δAL > 0 into the model. The unconditional LP blocking-delay distribution is then obtained as a weighted mixture over all occupancy states and all valid
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flow compositions as well as incorporating the AL. The PDF is given by, fDHP (x) = (1 − ρ)fG (x) +
B X k=1
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FG (x − Sn(k) ,AL ) − FG (x − Sn(k) ,AL − Tf ) Tf
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with Sn(k) ,AL = Sn(k) + (k − 1)δAL , gives the additional translation of the density by δAL . This formulation extends the single-packet blocking model to finite-capacity post-scheduler buffering by incorporating the stochastic occupancy of the TXR, the flow-dependent composition of the blocking packets and the AL. 2) Deterministic: The worst-case delay is obtained when the packets ahead of the arriving HP packet have the largest serialization time. With a post-scheduler TXR of capacity B packets, the HP packet can be blocked by up to B alreadydequeued LP packets in addition to the baseline processing delay. Therefore, the deterministic upper bound with the TXR is dDNC,TXR = dmax (5) proc + BTF + (B − 1)δAL . HP This bound extends the classical non-preemptive SP bound by replacing the single blocking packet with the largest possible set of B packets already admitted into the TXR along with the AL for B −1 gaps. Both updated models, Eq 4 and 5 can be reduced to their non-TXR form (Eq. 1, 2) by plugging B = 1 and δAL = 0. V. M EASUREMENT AND E VALUATION We use the single-NIC loopback method to measure the total latency at the switch witout the need for any clock synchronization [12]. Such a method uses the hardware timestamping mechanism in the NIC and reduces the error to ±8ns. For the 1G measurments we use an intel i350 and for the 10G measurements we use an intel x520 NIC. The LP flows can be generated by upto 4 seperate flows coming from seperate ports using iperf. The non-blocking parameters for the mean and variance of D0 are first collected over 10,000 samples without any LP traffic. Each real measurement is taken from at least 27,000 samples. A. TXR Size In this test all the LP flows transmit UDP packets such that their aggregate rate equals the link capacity of 1 Gbps. We then vary the packet size from 200 to 1500 bytes to ascertain that the TXR is indeed in terms of packets and not bytes, which is the case for priority queues. The results are shown in Fig. 3. If the TXR were defined in bytes, it would remain full in all three tests and the probe packet would be queued behind approximately the same number of bytes. This would produce nearly equal delays for all packet sizes, which is not observed. Instead, the delay decreases for smaller packets, showing that the probe packet is blocked by a fixed number of packets rather than a fixed number of bytes. Using the Tf values for each packet size, the observed separation between the curves gives a
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Delay (µs) Fig. 3. The TXR capacity is in packets, not bytes; Therefore, smaller packets experience a smaller overall delay. The models proposed in Eq. (4) and (5) shown in dashed lines fit the observed data in solid lines in contrast to the old model Eq. (1) in cross marks.
TXR size of B = 2 packets and δAL = 2.1µs. If the TXR size and AL is unknown, such a test can be applied to determine its value. Substituting these test conditions into Eq. (4), the aggregate load is ρ ≈ 1 and B = 2. Because the LP flows have identical packet sizes and rates within each experiment, n(k) has a single realization and pB ≈ 1. With these values, the model closely matches the measured CDFs for all three packet sizes as seen in Fig 3, comparing the dashed curves with the observed data in solid curves for each packet size. The vertical lines are the DNC bounds from Eq. 5 which also closely match the obtained results. In contrast, the old model (Eq. (1)) in cross marks is noticeably divergent from the observed values. The measurements presented above were obtained using an FS-S2805S 1G switch and show that the TXR capacity is packet-based rather than byte-based, with a default size of two packets for this switch. TABLE I We also conducted D EFAULT TXR SIZE AND AL additional measurements Switch Rate TXR AL across multiple 1G (Gb/s) Size (µs) 1 2 2.1 and 10G switches. The FS S2805S Dell S4048 10 3 1.7 default TXR sizes and AL FS S5850 10 3 1.3 Edgecore AS7726-32X 25 4 1.1 overhead observed in those experiments are summarized in Table I. Overall, the 10G and faster switches exhibit larger TXR sizes, which increases the potential blocking delay experienced by HP traffic under strict priority scheduling. The switches for which this discrepancy was not present were the Kontron D10 TSN switch and the Relyum TSN Bridge switch. Both devices support IEEE 802.1Qbu frame preemption, which requires a different egress architecture to stop an ongoing LP frame. However, for Kontron D10, we still measured an AL of 1.4µs. Thus the updated model with B = 1 is still useful for such cases. B. TCP Approximation (k,f )
Estimating the exact values of pk , χf , and πn is difficult under realistic traffic conditions. These quantities depend on complex inter-flow dynamics, flow burstiness, and packet interarrival times, which are not captured by the average flow rates alone. However, a useful approximation can be made when all LP flows are TCP flows with known rates. TCP traffic is inherently bursty because congestion-window transmission often releases multiple packets back-to-back after an acknowledgement or after the sender receives a window update, creating short packet trains rather than isolated packet arrivals.
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to set up a measurement in which the stationary values of pK can be directly controlled and independently verified. We leave further investigation of these effects and their parameter estimation for future work.
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VI. C ONCLUSION This paper identified a TXR-related discrepancy in packetdelay modeling for Ethernet switches that perform SP scheduling, where LP packets that have already been admitted into the post-scheduler transmit ring can continue to block an arriving HP packet. We provided both stochastic and deterministic models for this effect and validated them through SNC and DNC comparisons. By incorporating the post-scheduler TXR into both deterministic and stochastic analyses, the proposed models make DNC- and SNC-based evaluations more representative of deployed network switches. This brings analytical results closer to measured system behavior and can improve the reliability of latency guarantees and violation-probability estimates for systems that rely on strict-priority scheduling.
Delay (µs) Fig. 5. Effect of UDP burstiness on the measured delay for two packet sizes.
Moreover, for bulk TCP transfers, the packet size is typically close to the Maximum Transmission Unit (MTU). Thus, the serialization delay of each LP packet can be approximated by the MTU serialization delay, while the relative contribution of each flow can be inferred from its known rate. Fig. 4 compares this approximation with the measured CDFs for different aggregate TCP rates in Mbps on a link with 1Gbps capacity. Somewhat counterintuitively, the approximation improves as the aggregate LP rate decreases as the relative burst of the smaller flows is high. The approximation places the region before the linear part of the CDF as flat, which corresponds to setting p1 = 0. However, even with bursty TCP arrivals, there remains a small probability p1 that the probe packet is blocked by only one LP packet, which explains the discrepancy between the model and the empirical measurements. However, SNC provides delay bounds and the figure shows that the anayltical approximation does not violate the measured values, i.e., the dashed lines always remain below the solid ones. A posterior fit on the empirical data shows that p1 = 0.1ρ and p2 = 0.9ρ provides tigher bounds. C. UDP with Burst For UDP tests, iperf usually spaces packets approximately evenly over time. Its burst parameter can instead select how many packets are sent back-to-back before the sender waits for the next inter-arrival interval, while preserving the configured average flow rate. We perform four such tests for each of two packet sizes, 700 and 1500 bytes, using burst values of 1, 2, 10, and 100 packets. The LP flows were started at random times to allow for some interference between the batches of each flow. Fig. 5 shows that, when burstiness is low, the resulting delay distribution can be approximated by a linear model i.e., p1 = p2 = ρ2 . As burstiness increases, however, the probability that the TXR is filled increases, and the dominant blocking event shifts toward pB . In practice, it is difficult
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