Abstract

This paper presents a set of time efficient, sub-optimal heuristics to solve the problem of assigning cells to mobile switching centers (or, switches in short) for an effective location area (LA) planning in a mobile cellular network (MCN). A common objective of this NP-hard optimization problem, termed as cell-to-switch assignment (CSA) in the literature, is to minimize the hybrid cost, comprising handoff cost between adjacent cells, and the cable cost between cells and switches, subject to the constraint that the call volume to be handled by a switch should not exceed its traffic handling capacity. To solve CSA for a quasi-static/dynamic LA design, we need fast algorithms capable of producing acceptable solutions within a reasonable time. In this work, we first propose four variants (termed as heuristics III through VI) of our earlier heuristic (termed as heuristic II) and compare all of them with other published heuristics in respect of execution time and solution cost. Results indicate that though no single heuristic performs equally well with respect to both optimality and speed, heuristic IV is the best of the lot. Secondly, we modify the original CSA problem to include the factor of load balancing amongst switches (thereby minimizing unfairness), and propose a new CSA algorithm with load balancing (CALB), which emphasizes more on load balancing than on cost optimization. It is found that CALB is fast as heuristic VI, and performs extremely well in balancing the traffic amongst the switches, thereby increasing the overall scalability of MCNs against the increase in either mobile user density or per user traffic.

Keywords: Mobile communication; Cellular networks; Handoff; Location area partitioning; Hybrid cost; CSA; Load balancing; Optimization; Clustering and heuristics

Nomenclature

n

number of cells

m

number of switches

c_i

cell i, i  [1, n]

A_k

final cluster of cells around switch k (i.e., location area under switch k), k  [1, m]

x_ik

an assignment variable, i  [1, n], k  [1, m]

 

= 1 if c_i  A_k (i.e., cell i belongs to switch k),

 

= 0 otherwise

y_ij

another assignment variable, i, j  [1, n]

 

= 1 if c_i  A_k and c_j  A_k, i ≠ j, k  [1, m] (i.e., cell i and cell j both belong to switch k),

 

= 0 otherwise

h_ij

hand-off cost occurring between cell i and cell j, i, j  [1, n], i ≠ j

average hand-off cost occurring between cell i and its neighbors

 

= (∑_jh_ij)/(number of neighbors of cell i)

C_handoff

total handoff cost = ∑_i∑_jh_ij(1 − y_ij), i, j  [1, n], i ≠ j

C_ik

amortized cable cost for connecting cell i to switch k, i  [1, n], k  [1, m]

C_cable

total cable cost = ∑_i∑_kx_ikC_ik, i  [1, n], k  [1, m]

C_hybrid

total hybrid cost = [C_handoff + C_cable]

set of cells in the cluster around switch k after lth iteration, k  [1, m]

 

= A_k, when all iterations are finished

neighboring cells of , k  [1, m]

λ_i

traffic from cell i (in Erlangs), i  [1, n]

λ_av

average traffic from a cell (in Erlangs) = (1/n)∑_iλ_i, i  [1, n]

M_k

traffic handling capacity of switch k (in Erlangs), k  [1, m]

η^u

desired switch utilization factor of a switch = ∑_iλ_i/∑_kM_k, k  [1, m], (η^u  1)

modified traffic handling capacity of switch k = (M_kη^u), k  [1, m]

β_k

increment factor for switch k, k  [1, m]

η_k

actual utilization factor of switch k after load balancing, (η_k  1), k  [1, m]

utilization factor of switch k without load balancing, , k  [1, m]

σ²

mean square error (MSE) between η_k and , k  [1, m]

Article Outline

Nomenclature

1. Introduction

1.1. LA partitioning

1.2. CSA problem

1.3. Survey of related works

1.4. Motivation of present work

1.5. Organization of the paper

2. Problem formulation

2.1. CSA without load balancing

2.2. CSA with load balancing

3. Time efficient heuristics

3.1. Heuristic-II

3.2. Heuristic-III

3.3. Heuristic-IV

3.4. Heuristic-V

3.5. Heuristic-VI

3.6. An example

4. CSA with load balancing (CALB)

4.1. Algorithm

4.2. An example

5. Results and discussion

5.1. Time and cost comparison

5.2. Load balancing comparison

6. Conclusions

References

Vitae