Scenario of priority service for elastic traffic within the network slicing framework

Full Text

1. Introduction The rapid advancement of fifth-generation (5G) networks has significantly increased the demand for enhanced Quality of Service (QoS) from service providers. Organizations such as 3GPP and the GSM Association emphasize that 5G networks must support multiaccess capabilities, maintain low and predictable latency with minimal packet loss, and ensure high network resilience [1-3]. These stringent requirements have led to the development of flexible and adaptive network architectures capable of dynamically addressing these challenges [4-7]. One of the fundamental technologies that allows for this flexibility is Network Slicing (NS) [8-11]. NS allows mobile network operators to create multiple logically isolated and customizable network slices within a shared physical infrastructure, such as a base station (BS). These slices, referred to as Network Slice Instances (NSIs), can be dynamically deployed and removed based on real-time technical requirements, facilitating autonomous resource allocation without direct user involvement. Furthermore, NS enables service providers to manage QoS efficiently, enhancing fault tolerance and overall network reliability [12-15]. Each NSI is typically designed to support a specific category of service, such as best effort with minimum guarantee (BG), guaranteed bit rate (GB), or best effort (BE). BG and BE services generate elastic traffic with variable service duration, while GB services generate streaming traffic with fixed duration [16, 17]. © 2026 A. A. Tazaeva, E. V. Markova This work is licensed under a Creative Commons “Attribution-NonCommercial 4.0 International” license. This paper proposes a model for the joint servicing of two types of traffic, streaming and elastic with minimum guarantee, within a 5G network utilizing the NS framework. In addition, it evaluates key performance metrics to assess the efficiency of the model. The remainder of this paper is structured as follows. Section 2 introduces the radio admission control (RAC) scheme for a 5G network, formulated as a queueing system (QS) managing both streaming and elastic traffic. The analysis includes transition intensity diagrams, an infinitesimal generator, and calculations of key performance measures. Finally, Section 3 presents the conclusions. 2. System model Consider the operation of a base station (BS) cell within a network with a total capacity of C [capacity units, c.u.]. This capacity is distributed between two NSIs, each with capacities C1 and C2, respectively, k=1 where ∑2 Ck ⩾ C. The capacity Ck allocated to NSI k consists of two parts: a guaranteed capacity Qk and a shared capacity available to other NSIs, expressed as Ck - Qk, for k = 1, 2. The guaranteed k=1 capacities satisfy the condition ∑2 Qk ⩽ C, where 0 < Qk ⩽ Ck ⩽ C, for k = 1, 2. 1 We assume that the first NSI is for services generating streaming traffic (first-type requests), while the second NSI accommodates services generating elastic traffic (second-type requests). The arrival process for service requests follows a Poisson distribution with an arrival rate k, where k = 1, 2. The service time for first-type requests is exponentially distributed with a mean of -1. In contrast, the duration of the service for second-type requests depends on the system load and the average file length . Each first-type request requires b1 c.u., constrained by b1 ⩽ Q1. Similarly, each second-type request requires a minimum allocation of bmin c.u., where bmin ⩽ Q2. For simplicity, we set b1 = bmin = 1. 2 2 2 Let nk denote the number of active requests in NSI k (k = 1, 2) when the system is in state n = (n1, n2). Given the elastic nature of second-type traffic, the number of occupied capacity units is defined as n b2(n1, n2) = min(C - b1n1, C2) , 2 2 where bmin ⩽ b2(n1, n2) ⩽ C2. The corresponding service time for second-type requests is determined by -1(n1, n2) = n2 . 2 The key parameters are summarized in Table 1. b2(n1, n2) Now, let us analyze the request admission process in the system. When a new first-type request arrives, the following conditions apply: 1 o The request is admitted if the number of ongoing first-type requests is below the maximum allowable limit, given by Nmax = C1/b1, and there are sufficient available resources, specifically at least b1 capacity units. 1 o If the number of first-type requests is below the threshold supported by the guaranteed capacity, i.e., Ng = Q1/b1, but available resources are insufficient (less than b1), the request can still be accepted by interrupting a second-type request, provided that at least one second-type request exists within the guaranteed capacity Q1. o If neither of the above conditions is met, the request is blocked. The radio admission control mechanism for second-type requests is structured as follows: o The request is admitted if the number of ongoing second-type requests is below the maximum 2 2 permissible limit, given by Nmax = C2/bmin, and there are sufficient available resources, 2 specifically at least bmin capacity units. o If the number of second-type requests is below the threshold supported by the guaranteed capacity, i.e., Ng = Q2/bmin, but available resources are insufficient (less than bmin), the request 2 2 2 can still be accepted by interrupting a first-type request, provided that at least one first-type request exists within the guaranteed capacity Q2. Summary of key parameters Table 1 Notation Description C The BS’s total network capacity (capacity units, c.u.). Ck The k-th NSI’s overall network capacity, k ∈ {1, 2}, C1 + C2 ⩾ C (c.u.). Qk The k-th NSI’s guaranteed network capacity, Qk ⩽ Ck, Q1 + Q2 ⩽ C (c.u.). k The arrival rate of requests in k-th NSI, k ∈ {1, 2} (requests per unit of time). 1 -1 The average service time of one request at the first NSI (t.u.). The average length of the transmitted file (c.u. × t.u.). b1 The number of resource units required to serve each request of the first type (c.u.). b min 2 The minimal number of resource units required to serve each request of the second type (c.u.). nk The number of requests in k-th NSI, k ∈ {1, 2} (-). Nmax The maximum number of requests in k-th NSI, Nmax = C1/b1, k Nmax 1 min 2 = C2/b2 (-). N k g The maximum number of requests that can be served using guaranteed network capacity of k-th NSI (-). 2 b2(n1, n2) The number of resource units available for servicing each request of the second type in the state (n1, n2), bmin ⩽ b2(n1, n2) ⩽ C2 (c.u.). o If neither of these conditions is met, the second-type request is blocked. In cases where resources are insufficient, service interruption for first-type requests can occur through two mechanisms: 2 2 7. If the number of ongoing second-type requests is below the guaranteed threshold, i.e., n2 < Ng, a first-type request is interrupted to free up the minimum required resources, bmin, necessary for accommodating a second-type request. 8. If the number of ongoing second-type requests remains below the guaranteed threshold, i.e., 2 n2 < Ng, all second-type requests utilizing the guaranteed capacity Q2 are interrupted. This study focuses on the second scenario. The system operation is illustrated schematically in Figure 1. 3. Mathematical model The system behavior is described by a two-dimensional Markov process (MP) {(X1(t), X2(t)), t > 0}, where Xk(t) represents the number of k type requests in the system at time t, k = 1, 2, over the state space X: X = {(n1, n2) ∶ 0 ⩽ n1 ⩽ Nmax ∧ 0 ⩽ n2 ⩽ Nmax∧n1b1+ 1 2 2 +n2bmin ⩽ C ∧ n2b2(n1, n2) ⋅ I(n2 ⩾ 1) ⩾ Q2}, where I is a characteristic function I(P) = 1, if the condition is satisfied, { 0, if the condition is not satisfied. П П Figure 1. System model representation i The state space X includes few subsets: interruption subset Vk, admission subset Sk, and blocking subset Bk, where i, k ∈ {1, 2}, i ≠ k. Based on the sets, the transition intensity diagram can be represented in the following form (Figure 2). The interruption subset V2, V1 , represents the system states where the service of arriving k-type 1 2 request has priority over the service of i-type request (in other words, states where the service of i-type request can be interrupted to service one arriving k type request): 1 V2 = {(n1, n2) ∈ X ∶ n2 = 0 ∧ n2b2(n1, n2) < Q2}, V1 = {(n1, n2) ∈ X ∶ n1 < Ng ∧ n1b1 + n2bmin = C}. 2 1 2 The admission subset Sk, k = 1, 2, represents the system states where k-type request will be accepted for service in the k-th NSI: S1 = V1 ∪ {(n1, n2) ∈ X ∶ (0 ⩽ n1 < Nmax ∧ (n1 + 1)b1+ 2 1 + n2bmin ⩽ C ∧ n2 = 0) ∨ (0 ⩽ n1 < Nmax ∧ (n1 + 1)b1+ 2 1 2 + n2bmin ⩽ C ∧ n2 > 0 ∧ n2b2(n1, n2) > Q2)}, S2 = V2 ∪ {(n1, n2) ∈ X ∶ 0 ⩽ n2 < Nmax ∧ n1b1 + (n2 + 1)bmin ⩽ C}. 1 2 2 The blocking subset Bk, k = 1, 2, represents the system states where arriving k-type requests will be blocked by the system due to insufficient available resources in the k-th NSI: B1 = {(n1, n2) ∈ X ∶ n1 = Nmax ∨ (Ng ⩽ n1 < Nmax∧ 1 1 1 2 ∧ (n1 + 1)b1 + n2bmin > C) ∨ (n2 > 0 ∧ n2b2(n1 + 1, n2) < Q2)}. Figure 2. Scheme of the transition intensity diagram 2 B2 = {(n1, n2) ∈ X ∶ (n2 = Nmax)∨ ∨ (Ng ⩽ n2 < Nmax ∧ n1b1 + (n2 + 1)bmin > C)}. 2 2 2 According to the diagram of transition intensities (Figure 3), the considered process is described by the following system of equilibrium equations: p(n1, n2) ⋅ ( 2 ⋅ I{(n1, n2) ∈ S2/V2} + 1 ⋅ I{(n1, n2) ∈ V1} 1 2 + 1 ⋅ I{(n1, n2) ∈ S1/V1} + 2 ⋅ I{(n1, n2) ∈ V2} 2 1 + n2 2 ⋅ I{n2 > 0} + n1 1 ⋅ I{n1 > 0}) = [ 1 ⋅ p(n1 - 1, n2) + 2 ⋅ p(n1, n2 - 1) + (n1 + 1) 1 ⋅ p(n1 + 1, n2) + (n2 + 1) 2 ⋅ p(n1, n2 + 1)], where p(n1, n2), n ∈ X - stationary probability distribution of system states. Due to the implementation of the mechanism for interrupting the service of requests, the process {(X1(t), X2(t)), t > 0}, describing the considered system, is not a reversible Markov process. Therefore, the system’s stationary probability distribution p = {p(n1, n2), (n1, n2) ∈ X} can be computed using the numerical solution of the equilibrium equations system pT ⋅ A = 0T , pT ⋅ 1 = 1, where A is the infinitesimal generator, and the elements a((n1, n2), (n′ , n′ )) of this generator are determined by the 1 2 following formulas: Figure 3. The diagram of transition intensities for an arbitrary system state (n1, n2) ⎧ 1, n′ = n1 + 1, n′ = n2, (n1, n2) ∈ S1/V1, ⎪ 1 2 2 ⎪ 1, n′ = n1 + 1, n′ = n2 - 1, (n1, n2) ∈ V1, ⎪ 1 2 2 ⎪ ′ ′ 2 ⎪ 2, n1 = n1, n2 = n2 + 1, (n1, n2) ∈ S2/V1, ⎪ ′ C Q2 ′ 2 ′ ′ ⎪ 2, n1 = b - bmin , n2 = 1, (n1, n2) ∈ V1, a((n1, n2), (n1, n2)) = ⎨ 1 2 ⎪n1 1, n′ = n1 - 1, n′ = n2, n1 > 0, 1 2 ⎪ ⎪n2 2, n′ = n1, n′ = n2 - 1, n2 > 0, ⎪ 1 2 ⎪ ′ ′ where ⎪ , n1 = n1, n2 = n2, ⎪ ⎩0, otherwise, = -( 1⋅I{(n1, n2) ∈ S1}+ 2⋅I{(n1, n2) ∈ S2}+n1 1I{(n1, n2) ∈ X ∶ n1 > 0}+n2 2⋅I{(n1, n2) ∈ X ∶ n2 > 0}). 4. The main performance measures The main performance measures of the model are the following: - The mean number Nk of k-type requests served in the k-th NSI Nk = ∑ (n1,n2)∈X nk ⋅ p(n1, n2), k = 1, 2. i - The service interruption probability k of i type requests served in the i-th NSI when new k-type request arrives at the system i k = ∑ p(n1, n2), i, k = 1, 2, i ≠ k. i (n1,n2)∈Vk o The accepting probability Sk of k-th type request for service at k-th NSI Sk = ∑ p(n1, n2), k = 1, 2. (n1,n2)∈Sk o The blocking probability Bk of k-th type request 5. Results Bk = 1 - Sk = ∑ (n1,n2)∈Bk p(n1, n2), k = 1, 2. Let us now proceed to the numerical analysis. As a case study of a system supporting the joint handling of streaming and elastic traffic, we could consider a 5G network that provides both enhanced Mobile Broadband (eMBB) and Ultra-Reliable Low-Latency Communication (URLLC) services. In this context, eMBB corresponds to elastic traffic, while URLLC represents streaming traffic. We examine how key performance metrics-such as the mean number of active k-type requests, service interruption probability, accepting probability, and blocking probability-vary with changes in the arrival rate, for example, first-type requests. The parameters used in this numerical example are summarized in Table 2. Main parameters of the numerical example Table 2 Notation Value C 25 C1 20 C2 15 Q1 13 Q2 10 1 0 → 120 2 100 1 1 1.5 2 b1 = bmin 1 i Figure 4 presents the dependence of the service interruption probability k on the arrival rate 1. The plot demonstrates that, for the first-type of requests, the interruption probability increases slightly as 1 grows. On the contrary, for the second-type requests the probability of interruption increases sharply at first, and then also decreases sharply with an increase in the value of 1 and eventually approaches a stable value. This behavior occurs due to the fact that the intensity of the second-type requests is high, and they immediately occupy almost the entire system capacity, and therefore, when first-type requests arrival at the system, the guaranteed network capacity is released and service is interrupted. However, since the number of the second-type requests that can be interrupted is limited by the threshold value of Q1, then there is a decrease in the interruption probability. Figure 4. Dependence of the interruption probability on the arrival rate of the first-type requests Figure 5. Dependence of the accepting probability on the arrival rate of the first-type requests Figure 6. Dependence of the blocking probability on the arrival rate of the first-type requests Figure 7. Dependence of the mean number of serviced requests on the arrival rate of the first-type requests Let’s consider the behavior of the accepting probability Sk for each type of requests, depending on the first-type requests arrival rate, 1. As shown in Figure 5, at the initial moment of time, with a small 1, the accepting probability for the first-type requests is maximum and tends to unity, since requests of each type occupy the capacity of the corresponding NSI and do not affect the QoS for each other. As the arrival rate of requests increases, the accepting probability for both types of requests decreases rapidly. However, since the arrival rate of the second-type requests, ( 2), remains unchanged, the decrease in S2 is less pronounced in the graph. A similar trend is observed in Figure 6, which depicts the blocking probabilities. As 1 increases, the blocking probability B1 grows correspondingly, while the blocking probability B2 remains nearly constant due to the fixed arrival rate 2. 2 We now turn to the most insightful graph, which illustrates the dependence of the mean number of serviced requests Nk, for k = 1, 2, on the arrival rate 1 of the first-type requests. As shown in Figure 7, when no first-type requests are present in the system, second-type requests utilize the entire portion of capacity C2 = 15 allocated to them and the number of second-type requests served in the system tends to the maximum value Nmax = 15. As first-type requests begin to arrive, the number of serviced second-type requests N2 gradually decreases. Under conditions of full system load, the number of serviced requests for both types converges to their respective guaranteed levels Ng = 13 and Ng = 10. 1 2 6. Discussion The obtained results highlight the interaction between streaming and elastic traffic in a sliced 5G network. The interruption probability of elastic flows increases sharply in the low-to-medium 1 regime, but then stabilizes as the guaranteed resources Q1 and Q2 become dominant. This confirms the importance of guaranteed quotas for maintaining predictable service. Compared to earlier work on preemption-based prioritization [12], our approach explicitly models admission control with guaranteed resource allocation. The findings are consistent with survey studies on slicing performance [4, 5, 7], while extending them by quantifying blocking and interruption trade- offs. From a practical perspective, the model illustrates how operators can tune Q1 and Q2 to balance eMBB and URLLC requirements. Such tuning directly impacts blocking probabilities and guarantees acceptable QoS under varying load conditions. This insight is useful for SLA negotiation and capacity planning. Naturally, the model has limitations. It assumes Poisson arrivals, exponential service times, and only two slices. Correlations between traffic types, mobility patterns, or more complex slice hierarchies are not captured. Moreover, the interruption mechanism is simplified, focusing only on guaranteed thresholds. Future extensions could include machine-learning-based controllers for adaptive RAC [18, 19], as well as integration with edge computing and 6G scenarios [16, 20]. 7. Conclusions This paper introduced a radio admission control model for 5G network slicing with priority interruption. The model differentiates between streaming and elastic traffic and evaluates key performance metrics such as blocking, accepting, and interruption probabilities, as well as mean numbers of active requests. The results demonstrate that the proposed mechanism successfully captures the trade-offs between heterogeneous traffic classes. The analysis provides operators with quantitative guidelines for configuring guaranteed capacities and balancing competing QoS requirements. The presented framework thus offers a foundation for more efficient and fair resource allocation strategies in slice- aware wireless networks.

About the authors

Anastasia A. Tazaeva

RUDN University

Author for correspondence.
Email: tazaeva081@gmail.com
ORCID iD: 0009-0001-4065-0847

Student of Department of Probability Theory and Cyber Security

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Ekaterina V. Markova

RUDN University; Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences

Email: markova-ev@rudn.ru
ORCID iD: 0000-0002-7876-2801
Scopus Author ID: 56315828200

Ph.D. in Physics and Mathematics, Associate Professor of Department of Probability Theory and Cyber Security of RUDN University

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation; 44 Vavilova St, bldg 2, Moscow, 119333, Russian Federation

References

Supplementary files