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Erlang Model for Multi-type Data Flow

Liuquan Yao, Pei Yang, Zhichao Liu, Wenyan Li, Jianghua Liu, Zhi-Ming Ma

TL;DR

The paper addresses MDF in modern networks where users demand diverse data types over time. It develops three time-dependent demand regimes (non-tolerance, tolerance, delay) and shows that, under time discretization, MDF aligns with a discrete EMLM skeleton; it then provides closed-form-like expressions for blocking probabilities in each regime and proves that MDF with memoryless service converges to EMLM as the time step vanishes. A practical pre-allocation algorithm is proposed to determine the minimal resources needed to meet a target distortion or blocking level, supported by a toy example that confirms the theoretical results. The work advances capacity planning for base stations under MDF by unifying time-varying demand modelling with Erlang-based loss models, enabling efficient, low-withed resource provisioning in 5G-era networks.

Abstract

With the development of information technology, requirements for data flow have become diverse. When multi-type data flow (MDF) is used, games, videos, calls, etc. are all requirements. There may be a constant switch between these requirements, and also multiple requirements at the same time. Therefore, the demands of users change over time, which makes traditional teletraffic analysis not directly applicable. This paper proposes probabilistic models for the requirement of MDF, and analyzes in three states: non-tolerance, tolerance and delay. When the requirement random variables are co-distributed with respect to time, we prove the practicability of the Erlang Multirate Loss Model (EMLM) from a mathematical perspective by discretizing time and error analysis. An algorithm of pre-allocating resources is given to guild the construction of base resources.

Erlang Model for Multi-type Data Flow

TL;DR

The paper addresses MDF in modern networks where users demand diverse data types over time. It develops three time-dependent demand regimes (non-tolerance, tolerance, delay) and shows that, under time discretization, MDF aligns with a discrete EMLM skeleton; it then provides closed-form-like expressions for blocking probabilities in each regime and proves that MDF with memoryless service converges to EMLM as the time step vanishes. A practical pre-allocation algorithm is proposed to determine the minimal resources needed to meet a target distortion or blocking level, supported by a toy example that confirms the theoretical results. The work advances capacity planning for base stations under MDF by unifying time-varying demand modelling with Erlang-based loss models, enabling efficient, low-withed resource provisioning in 5G-era networks.

Abstract

With the development of information technology, requirements for data flow have become diverse. When multi-type data flow (MDF) is used, games, videos, calls, etc. are all requirements. There may be a constant switch between these requirements, and also multiple requirements at the same time. Therefore, the demands of users change over time, which makes traditional teletraffic analysis not directly applicable. This paper proposes probabilistic models for the requirement of MDF, and analyzes in three states: non-tolerance, tolerance and delay. When the requirement random variables are co-distributed with respect to time, we prove the practicability of the Erlang Multirate Loss Model (EMLM) from a mathematical perspective by discretizing time and error analysis. An algorithm of pre-allocating resources is given to guild the construction of base resources.

Paper Structure

This paper contains 13 sections, 3 theorems, 17 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. Probability Models for Time-dependent MDF
  3. Non-tolerance
  4. Tolerance
  5. Delay
  6. Erlang Formula for MDF
  7. Erlang Multirate Loss Model
  8. Distribution analysis for $S_{\lambda, p,t_s}$
  9. Blocking Probability for $MDF(\lambda,p,t_s)$
  10. Simulation
  11. The Algorithm for Pre-allocating Resources
  12. A Toy Example
  13. Conclusion

Key Result

Theorem 3.1

The distribution of $S_{\lambda,p,t_s}$ is where $P^2_k\sim Poi(\lambda t_s a_kN(1-pt_s/\ln p))$ are independent. Furthermore, if $\lim_{t_s\to 0} -\ln p/t_s=\mu$, then $S_{\lambda,p,t_s}$ is close to the $S_{EMLM}$ with arrival rate $\lambda$ and $Exp(\mu)$ distributed required time, i.e.

Figures (1)

  • Figure 1: Blocking Probability Curve

Theorems & Definitions (5)

  • Definition 3.1
  • Remark 3.1
  • Theorem 3.1
  • Corollary 3.1
  • Theorem 3.2